4t ESO/4.02 POTÈNCIES I ARRELS/4.02.1 Potències i operacions 4.02.1.00 TEORIA Potència d'exponent positiu

POTÈNCIA D'EXPONENT POSITIU

Expressen un producte reiterat:

3⁵ = 3·3·3·3·3 = 243
Si es calcula la potència d'un nombre negatiu:

Si l'exponent és parell: positiva. (-3)⁴ = 81
Si l'exponent és imparell: negativa. (-3)³ = -27

A la calculadora, per exponents superiors a 2, es fan servir les tecles: shift ×(multiplicat); ^ ; x^■

]]> 0.0000000 0.0000000 0 4.02.1.01Q PotènciesNaturalsDeNombrePositiu Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math»
Dona el resultat en forma de nombre

]]>

#f shift × #e
#f ^ #e
#f x^■ #e

]]> 4.02.1.02Q PotènciaParellaDeNombreNegatiu Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mstyle»«/math»
Dona el resultat en forma de nombre

( #f ) shift × #e
( #f ) ^ #e
( #f ) x^■ #e

NO ET DEIXIS ELS PARÈNTESIS

Quan la potència és parella, el resultat sempre és positiu.

]]> 4.02.1.03Q PotènciaImparellaDeNombreNegatiu Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mstyle»«/math»
Dona el resultat en forma de nombre

( #f ) shift × #e
( #f ) ^ #e
( #f ) x^■ #e

NO ET DEIXIS ELS PARÈNTESIS

La potència imparella d'un nombre negatiu és negativa.

]]> 4.02.1.04Q PotènciaAleatòriaDeNombreNegatiu Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mstyle»«/math»
Dona el resultat en forma de nombre

( #f ) shift × #e
( #f ) ^ #e
( #f ) x^■ #e

NO ET DEIXIS ELS PARÈNTESIS

]]> 4.02.1.05 TEORIA Potència d'exponent negatiu

POTÈNCIA D'EXPONENT NEGATIU

Obliguen a calcular l'invers del nombre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨italic¨»-«/mo»«mi»n«/mi»«/mrow»«/msup»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mn mathvariant=¨italic¨»1«/mn»«mi»a«/mi»«/mfrac»«/mfenced»«mi»n«/mi»«/msup»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨italic¨ mathcolor=¨#00007F¨»3«/mn»«mrow»«mo mathvariant=¨italic¨»-«/mo»«mn mathvariant=¨italic¨»5«/mn»«/mrow»«/msup»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mn mathvariant=¨italic¨»1«/mn»«mn mathvariant=¨italic¨»3«/mn»«/mfrac»«/mfenced»«mn mathvariant=¨italic¨»5«/mn»«/msup»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»;«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mn mathvariant=¨italic¨»2«/mn»«mn mathvariant=¨italic¨»5«/mn»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨italic¨»-«/mo»«mn mathvariant=¨italic¨»3«/mn»«/mrow»«/msup»«mo mathvariant=¨italic¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mn mathvariant=¨italic¨»5«/mn»«mn mathvariant=¨italic¨»2«/mn»«/mfrac»«/mfenced»«mn mathvariant=¨italic¨»3«/mn»«/msup»«/math»

]]> 0.0000000 0.0000000 0 4.02.1.06Q PotènciaNegativaDeNombrePositiu Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»
Dona el resultat en forma d'enter o de fracció sense exponent.

]]> La potència (positiva, negativa, parella o imparella) d'un nombre POSITIU és sempre POSITIVA.

]]> 1.0000000 0.2500000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced close="|" open="|"><mi>e</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfenced close="|" open="|"><mi>f</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>f</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>residu</mi><mo>(</mo><mi>e2</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>Com</mi><mo> </mo><mi>que</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>exponent</mi><mo> </mo><mi>és</mi><mo> </mo><mi>PARELL</mi><mo>,</mo><mo> </mo><mi>el</mi><mo> </mo><mi>resultat</mi><mo> </mo><mi>és</mi><mo> </mo><mi>sempre</mi><mo> </mo><mi>POSITIU</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>La</mi><mo> </mo><mi>potència</mi><mo> </mo><mi>IMPARELLA</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>nombre</mi><mo> </mo><mi>negatiu</mi><mo> </mo><mi>és</mi><mo> </mo><mi>NEGATIVA</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>59049</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>La</ms><mo> </mo><ms>potència</ms><mo> </mo><ms>IMPARELLA</ms><mo> </mo><ms>d'un</ms><mo> </mo><ms>nombre</ms><mo> </mo><ms>negatiu,</ms><mo> </mo><ms>és</ms><mo> </mo><ms>NEGATIVA</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que la potència és negativa, calculem l'invers:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mfrac»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mstyle»«/math»

i elevem

]]> 4.02.1.07Q PotènciaNegativaDeNombreNegatiu Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mstyle»«/math»
Dona el resultat en forma d'enter o de fracció sense exponent.

]]> #t

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced close="|" open="|"><mi>e</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfenced close="|" open="|"><mi>f</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>f</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>residu</mi><mo>(</mo><mi>e2</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>Com</mi><mo> </mo><mi>que</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>exponent</mi><mo> </mo><mi>és</mi><mo> </mo><mi>PARELL</mi><mo>,</mo><mo> </mo><mi>el</mi><mo> </mo><mi>resultat</mi><mo> </mo><mi>és</mi><mo> </mo><mi>sempre</mi><mo> </mo><mi>POSITIU</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>La</mi><mo> </mo><mi>potència</mi><mo> </mo><mi>IMPARELLA</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>nombre</mi><mo> </mo><mi>negatiu</mi><mo> </mo><mi>és</mi><mo> </mo><mi>NEGATIVA</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>59049</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>La</ms><mo> </mo><ms>potència</ms><mo> </mo><ms>IMPARELLA</ms><mo> </mo><ms>d'un</ms><mo> </mo><ms>nombre</ms><mo> </mo><ms>negatiu,</ms><mo> </mo><ms>és</ms><mo> </mo><ms>NEGATIVA</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que la potència és negativa, calculem l'invers:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mo»-«/mo»«mfrac»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/math»

]]> Ara ja pots aplicar que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced mathcolor=¨#007F00¨»«mrow»«mo»-«/mo»«mfrac»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mfrac mathcolor=¨#007F00¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 4.02.1.08Q PotènciaNegativaDeFraccióPositiva Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mstyle»«/math»
Dona el resultat en forma d'enter o de fracció sense exponent.

]]> La potència (positiva, negativa, parella o imparella) d'un nombre POSITIU és sempre POSITIVA.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced close="|" open="|"><mi>e</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfenced close="|" open="|"><mi>f</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>f</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>residu</mi><mo>(</mo><mi>e2</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>Com</mi><mo> </mo><mi>que</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>exponent</mi><mo> </mo><mi>és</mi><mo> </mo><mi>PARELL</mi><mo>,</mo><mo> </mo><mi>el</mi><mo> </mo><mi>resultat</mi><mo> </mo><mi>és</mi><mo> </mo><mi>sempre</mi><mo> </mo><mi>POSITIU</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>La</mi><mo> </mo><mi>potència</mi><mo> </mo><mi>IMPARELLA</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>nombre</mi><mo> </mo><mi>negatiu</mi><mo> </mo><mi>és</mi><mo> </mo><mi>NEGATIVA</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>343</mn><mn>216</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>La</ms><mo> </mo><ms>potència</ms><mo> </mo><ms>IMPARELLA</ms><mo> </mo><ms>d'un</ms><mo> </mo><ms>nombre</ms><mo> </mo><ms>negatiu</ms><mo> </mo><ms>és</ms><mo> </mo><ms>NEGATIVA</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que la potència és negativa, calculem l'invers:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/math»

]]> Ara ja pots aplicar que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced mathcolor=¨#007F00¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold-italic¨»b«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold-italic¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 4.02.1.09Q PotènciaNegativaDeFraccióNegativa Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mstyle»«/math»
Dona el resultat en forma d'enter o de fracció sense exponent.

]]> #t

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced close="|" open="|"><mi>e</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mo>-</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfenced close="|" open="|"><mi>f</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>f</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>residu</mi><mo>(</mo><mi>e2</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>Com</mi><mo> </mo><mi>que</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>exponent</mi><mo> </mo><mi>és</mi><mo> </mo><mi>PARELL</mi><mo>,</mo><mo> </mo><mi>el</mi><mo> </mo><mi>resultat</mi><mo> </mo><mi>és</mi><mo> </mo><mi>sempre</mi><mo> </mo><mi>POSITIU</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>t</mi><mo>=</mo><mo>"</mo><mi>La</mi><mo> </mo><mi>potència</mi><mo> </mo><mi>IMPARELLA</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>nombre</mi><mo> </mo><mi>negatiu</mi><mo> </mo><mi>és</mi><mo> </mo><mi>NEGATIVA</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>9</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>125</mn><mn>729</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>La</ms><mo> </mo><ms>potència</ms><mo> </mo><ms>IMPARELLA</ms><mo> </mo><ms>d'un</ms><mo> </mo><ms>nombre</ms><mo> </mo><ms>negatiu</ms><mo> </mo><ms>és</ms><mo> </mo><ms>NEGATIVA</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que la potència és negativa, calculem l'invers:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mo»-«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mo»-«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/math»

]]> Ara ja pots aplicar que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced mathcolor=¨#007F00¨»«mrow»«mo»-«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold-italic¨»b«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold-italic¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 4.02.1.10 TEORIA Producte de potències

Productes de potències

Per multiplicar potències de la mateixa base,

cal SUMAR els exponent:

3⁵ · 3⁸ = 3¹³
3⁹ · 3^-11 = 3^-2

]]> 0.0000000 0.0000000 0 4.02.1.11Q ProductePotènciesNaturalsDe x Calcula el producte «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math»
Dona el resultat en forma de potència (x elevat a un nombre)

]]> 4.02.1.12Q ProductePotènciesNaturalsDe x_2 Calcula el producte «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
Dona el resultat en forma de potència (x elevat a un nombre)

]]> 4.02.1.15Q ProductePotènciesNaturalsDe a Calcula el producte «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math»

]]> 4.02.1.21Q ProductePotènciesEnteresDe x Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
Dona el resultat en forma de potència (x elevat a un nombre positiu; si és negatiu, cal escriure l'invers)

]]> 1.0000000 0.5000000 0 0 #r_1 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mi>x</mi><mi>f</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>+</mo><mi>f</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>+</mo><mi>f</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>&quot;</mo><mi>nul</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>&quot;</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>&quot;</mo><mi>cal</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>/</mo><msup><mi>x</mi><mfenced close="&verbar;" open="&verbar;"><mrow><mi>e</mi><mo>+</mo><mi>f</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiu</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>no</ms><mo> </mo><ms>cal</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Per a multiplicar potències, n'hi ha prou amb SUMAR els exponents.
L'exponent de x és doncs (#e) + (#f).
Com que (#e) + (#f) és #s, #w escriure l'invers #z.

]]> 4.02.1.22Q ProductePotènciesEnteresDe x_2 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math»
Dona el resultat en forma de potència (x elevat a un nombre positiu; si és negatiu, cal escriure l'invers)

]]> 0.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mi>x</mi><mi>f</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>+</mo><mi>f</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>+</mo><mi>f</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>nul</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>/</mo><msup><mi>x</mi><mfenced close="|" open="|"><mrow><mi>e</mi><mo>+</mo><mi>f</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiu</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>no</ms><mo> </mo><ms>cal</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a multiplicar potències, n'hi ha prou amb SUMAR els exponents.
L'exponent x és doncs (#e) + (#f).
Com que (#e) + (#f) és #s, #w escriure l'invers #z.

]]> 4.02.1.25Q ProductePotènciesEnteresDe a Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»m«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»m«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: Enter o fracció

]]> 0.0000000 0.5000000 0 0 #r_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>m</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mi>m</mi><mi>f</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>+</mo><mi>f</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>+</mo><mi>f</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>nul</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>/</mo><msup><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi></mtd></mtr></mtable></mfenced><mfenced close="|" open="|"><mrow><mi>e</mi><mo>+</mo><mi>f</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2401</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cal</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn></mtd></mtr></mtable></mfenced><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>49</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a multiplicar potències, n'hi ha prou amb SUMAR els exponents.
L'exponent de #m és doncs (#e) + (#f).
Com que (#e) + (#f) és #s, #w escriure l'invers #z.

]]> 4.02.1.30 TEORIA Quocient de potències

Divisió de potències

Per DIVIDIR potències de la mateixa base,

cal RESTAR els exponents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»3«/mn»«mn»7«/mn»«/msup»«mo mathcolor=¨#00007F¨»:«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»3«/mn»«mn»2«/mn»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»3«/mn»«mrow»«mn»7«/mn»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»§#160;«/mo»«mo mathcolor=¨#00007F¨»=«/mo»«mo mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»3«/mn»«mn»5«/mn»«/msup»«mspace linebreak=¨newline¨/»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»5«/mn»«mn»4«/mn»«/msup»«mo mathcolor=¨#00007F¨»:«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»5«/mn»«mrow»«mo»-«/mo»«mn»3«/mn»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»5«/mn»«mrow»«mn»4«/mn»«mo»-«/mo»«mo»(«/mo»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«mo»§#160;«/mo»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»5«/mn»«mn»7«/mn»«/msup»«mspace linebreak=¨newline¨/»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»7«/mn»«mn»2«/mn»«/msup»«mo mathcolor=¨#00007F¨»:«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»7«/mn»«mn»5«/mn»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»7«/mn»«mrow»«mn»2«/mn»«mo»-«/mo»«mn»5«/mn»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»7«/mn»«mrow»«mo»-«/mo»«mn»3«/mn»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mn»1«/mn»«mn»7«/mn»«/mfrac»«/mfenced»«mn»3«/mn»«/msup»«/math»

]]> 0.0000000 0.0000000 0 4.02.1.31Q Quocient de potències naturals Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
Format del resultat: potència d'exponent positiu (x elevat a un nombre, o invers)

]]> ]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mi>x</mi><mi>f</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>-</mo><mi>f</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>-</mo><mi>f</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>nul</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>/</mo><msup><mi>x</mi><mfenced close="|" open="|"><mrow><mi>e</mi><mo>-</mo><mi>f</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cal</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>x</mi><mn>4</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>9</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>x</mi><mn>4</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal restar els exponents: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«/mrow»«/mstyle»«/math».

Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«/mrow»«/mstyle»«/math» és negatiu cal escriure «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mfrac»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mfrac»«/mfenced»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«/msup»«/mstyle»«/math»

]]> 4.02.1.32Q Quocient de potències naturals Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mstyle»«/math»
Format del resultat: potència d'exponent positiu (x elevat a un nombre, o invers)

]]> 4.02.1.41Q Quocient de potències enteres Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math»

Format del resultat: potència d'exponent positiu (x elevat a un nombre, o invers)

]]> 1.0000000 0.5000000 0 0 #r_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mi>e</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mi>x</mi><mi>f</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>-</mo><mi>f</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>-</mo><mi>f</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>zero</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><msup><mfenced><mfrac><mn>1</mn><mi>x</mi></mfrac></mfenced><mfenced close="|" open="|"><mrow><mi>e</mi><mo>-</mo><mi>f</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>x</mi><mn>9</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>8</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>x</mi><mn>17</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a dividir potències, n'hi ha prou amb RESTAR els exponents.
L'exponent de x en el resultat és doncs «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«/mrow»«/mstyle»«/math».
Atenció: restar un nombre negatiu és com sumar el seu valor absolut:
per exemple 6 - (-3) = 6 + 3 = 9; en canvi: 6 - 3 = 3.
Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«/mrow»«/mstyle»«/math» és #s, #w escriure l'invers #z.

]]> 4.02.1.42Q Quocient de potències enteres Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo»§#160;«/mo»«/mstyle»«/math»

Format del resultat: potència d'exponent positiu (x elevat a un nombre, o invers)

]]> 4.02.1.50 TEORIA Elevar potències

Elevar potències

Per ELEVAR una potència a una altra potència,

cal MULTIPLICAR els exponents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«msup»«mn»3«/mn»«mn»5«/mn»«/msup»«/mfenced»«mn»4«/mn»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»3«/mn»«mn»20«/mn»«/msup»«mspace linebreak=¨newline¨/»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«msup»«mn»2«/mn»«mn»4«/mn»«/msup»«/mfenced»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mn mathcolor=¨#00007F¨»2«/mn»«mrow»«mo»-«/mo»«mn»8«/mn»«/mrow»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/mfenced»«mn»8«/mn»«/msup»«/math»

]]> 0.0000000 0.0000000 0 4.02.1.51Q Elevar una potència natural Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«msup mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

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]]> 4.02.1.52Q Elevar a una potència entera Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«/mstyle»«/math» =

Format de la resposta: Potència d'exponent positiu

]]> 0.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>*</mo><mi>f</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>*</mo><mi>f</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>nul</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>/</mo><msup><mi>x</mi><mfenced close="|" open="|"><mrow><mi>e</mi><mo>*</mo><mi>f</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mfenced><msup><mi>x</mi><mi>e</mi></msup></mfenced><mi>f</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>35</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per elevar una potència a una altra potència, multipliquem els exponents.
L'exponent de la x és doncs (#e) · (#f).
Com que (#e) · (#f) és #s, #w escriure l'invers #z.

]]> 4.02.1.61Q OperacionsCombinadesPotènciesDe a Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»o«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/msup»«/mstyle»«/math»

Format de la resposta: Enter o fracció

]]> 1.0000000 0.5000000 0 0 #r_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>o</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mfenced><mrow><mfenced><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mi>o</mi><mo>+</mo><mi>p</mi></mrow></mfenced></mrow></mfenced><mo>*</mo><mi>q</mi></mtd></mtr></mtable><mfenced><mrow><mfenced close="|" open="|"><mi>e1</mi></mfenced><mo><</mo><mn>6</mn></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><mi>o</mi><mo>+</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_3</mi><mo>=</mo><mi>s_1</mi><mo>-</mo><mi>s_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s_3</mi><mo>*</mo><mi>q</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s_3</mi><mo>*</mo><mi>q</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>zero</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>"</mo><mo>,</mo><mo> </mo><mi>dona</mi><mo> </mo><mn>1</mn><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>"</mo><mi>cal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>/</mo><msup><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mfenced><mfenced close="|" open="|"><mrow><mi>s_3</mi><mo>*</mo><mi>q</mi></mrow></mfenced></msup></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mfenced><mfrac><mrow><msup><mi>a</mi><mi>m</mi></msup><mo>·</mo><msup><mi>a</mi><mi>n</mi></msup></mrow><mrow><msup><mi>a</mi><mi>p</mi></msup><mo>*</mo><msup><mi>a</mi><mi>o</mi></msup></mrow></mfrac></mfenced><mi>q</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1) Multiplica el numerador: #a^#m · #a^#n = #a^#s_1 (Suma els exponents)
2) Multiplica els denominadors: #a^#o · #a^#p = #a^#s_2 (Suma els exponents)
3) Divideix el numerador pel denominador: #a^#s_1 / #a^#s_2= #a^#s_3(Resta els exponents)
4) Eleva el resultat a #q (multiplica els exponents)

Com que (#s_3) · (#q) és #s, #w escriure l'invers #z.

]]> 4.02.1.62Q OperacionsCombinadesPotènciesDe x Calculeu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mfrac»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»o«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«/msup»«/mstyle»«/math»
Format de la resposta: potència d'exponent positiu de x

]]> 1.0000000 0.5000000 0 0 #r_1 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><mi>o</mi><mo>+</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_3</mi><mo>=</mo><mi>s_1</mi><mo>-</mo><mi>s_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s_3</mi><mo>*</mo><mi>q</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo> </mo><mi>cal</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol 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1) Multiplica el numerador: x^#m · x^#n = x^#s_1 (Suma els exponents)
2) Multiplica els denominadors: x^#o · x^#p =x^#s_2 (Suma els exponents)
3) Divideix el numerador pel denominador: x^#s_1 / x^#s_2= x^#s_3(Resta els exponents)
4) Eleva el resultat a #q (multiplica els exponents)

Com que (#s_3) · (#q) és #s, #w escriure l'invers #z.

]]> 4.02.1.63Q OperacionsCombinadesTrobarPotènciaDe x Per a quin valor de k es compleix aquesta igualtat?

«math xmlns="http://www.w3.org/1998/Math/MathML"»«msup»«mfenced»«mfrac»«mrow»«msup»«mi»x«/mi»«mi»k«/mi»«/msup»«mo»·«/mo»«msup»«mi»x«/mi»«mi»#n«/mi»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mi»#o«/mi»«/msup»«mo»·«/mo»«msup»«mi»x«/mi»«mi»#p«/mi»«/msup»«/mrow»«/mfrac»«/mfenced»«mi»#q«/mi»«/msup»«mo»=«/mo»«mi»#p_1«/mi»«/math»

Format de la resposta:3
]]> Calcula el membre de l'esquerra per igualar exponents:
1) Multiplica el numerador: x^k · x^#n = x^k+#n (Suma els exponents)
2) Multiplica els denominadors: x^#o · x^#p =x^#s_2 (Suma els exponents)
3) Divideix el numerador pel denominador: x^k+#n / x^#s_2= x^#s_3(Resta els exponents)
4) Eleva el resultat a #q (multiplica els exponents): x^#s_4
5) Resol l'equació#s_4 = #s_5 #j

]]> 0.0000000 0.5000000 0 0 #r_1 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_1</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 4.02.1.71 Potències d'exponent natural «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» {#1}^{#2} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» a^{#3} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«/mrow»«/mstyle»«/math» {#4}^{#5} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» a^{#6} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» {#7}^{#8} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»6«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» a^{#9}

Escriviu el resultat com una potència

]]> 9.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced><mi>b_1</mi></mfenced><mo>+</mo><mfenced><mi>d_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced><mi>b_2</mi></mfenced><mo>-</mo><mfenced><mi>d_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mi>d_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>b_4</mi><mo>+</mo><mi>d_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mi>b_5</mi><mo>-</mo><mi>d_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_6</mi><mo>=</mo><mi>b_6</mi><mo>*</mo><mi>d_6</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_2</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>d_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_3</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>d_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.02.1.72 Potències d'exponent enter «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» {#1}^{#2} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» a^{#3} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«msup mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» {#4}^{#5} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» a^{#6} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/msup»«/mrow»«/mfenced»«msup mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math»
{#7}^{#8} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»6«/mn»«/mrow»«/msup»«/mfenced»«msup mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d_«/mi»«mn mathvariant=¨bold¨»6«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«/mrow»«/mstyle»«/math» a^{#9}

Escriviu el resultat com una potència

]]> 9.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced><mi>b_1</mi></mfenced><mo>+</mo><mfenced><mi>d_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced><mi>b_2</mi></mfenced><mo>-</mo><mfenced><mi>d_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mi>d_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>b_4</mi><mo>+</mo><mi>d_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mi>b_5</mi><mo>-</mo><mi>d_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_6</mi><mo>=</mo><mi>b_6</mi><mo>*</mo><mi>d_6</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_2</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>d_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_3</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>d_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.02.1.81Q EscriureNombreComPotènciaPosit Escriu com a potència de #a el nombre #b:

#b = #a^{#1}

]]> 1.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>p</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b</mi><mo>></mo><mn>500</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo><</mo><mn>1000</mn></mrow></mfenced></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>729</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Fes la descomposició en factors

]]> 4.02.1.82Q EscriureNombreComPotènciaPosit_2 Escriu com a potència de #a el nombre #b:

#b = #a^{#1}

]]> 4.02.1.83Q EscriureNombreComPotènciaNegat Escriu com a potència de #a el nombre #b:

#b = #a^{#1}

]]> 1.0000000 0.1000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>p</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>32</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> Fes la descomposició en factors

]]> 4.02.1.84Q EscriureNombreComPotènciaNegat_2 Escriu com a potència de #a el nombre #b:

#b = #a^{#1}

]]> 4t ESO/4.02 POTÈNCIES I ARRELS/4.02.2 Arrels 4.02.2.110 TEORIA Definició arrel Arrel n-èsima

S'anomena arrel n-èsima del nombre x, el nombre y que elevat a n dona x: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»y«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«/math»

També es pot escriure com un exponent FRACCIONARI:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msup»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mfrac»«/msup»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.111Q Trobar l'índex Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»y«/mi»«/mrow»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«/mrow»«/mstyle»«/math», quin és el valor de n?

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mi>a</mi><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes la descomposició en factors de #y per trobar n

]]> Si fas la descomposició en factors de #y,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»

]]> 4.02.2.112Q Escriure y com arrel nèsima de x Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mstyle»«/math», escriu y com arrel n-èsima de x?

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>y</mi><mo>=</mo><mroot><mi>x</mi><mi>n</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mroot><mi>x</mi><mn>4</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'índex de l'arrel és l'exponent de y en l'expressió que et donen.

]]> 4.02.2.113Q Escriure a com arrel nèsima de x Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mstyle»«/math», escriu #a com l'arrel n-èsima de x

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>=</mo><mroot><mi>x</mi><mi>n</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>=</mo><mroot><mi>x</mi><mn>5</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'índex de l'arrel és l'exponent del #a en l'expressió que et donen.

]]> 4.02.2.114Q Traducció exponent fraccionari Escriu l'arrel que correspon a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mroot><msup><mi>x</mi><mi>m</mi></msup><mi>n</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mi>x</mi><mn>4</mn></msup><mn>5</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'índex de l'arrel és el denominador #n, i l'exponent de x és el numerador #m.

]]> 4.02.2.115Q Traducció d'arrel nèsima a exp.fraccionari Escriu l'arrel que correspon a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mroot><msup><mi>x</mi><mi>m</mi></msup><mi>n</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mi>x</mi><mn>4</mn></msup><mn>5</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'índex de l'arrel és el denominador #n, i l'exponent de x és el numerador #m.

]]> 4.02.2.116Q Traducció d'arrel nèsima a exp.fraccionari Quin és l'exponent fraccionari que correspon a x en l'expressió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mroot»«/mstyle»«/math»

Format: escriu només l'exponent, no la x.

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>m</mi><mi>n</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mi>x</mi><mn>4</mn></msup><mn>5</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'índex de l'arrel és el denominador #n, i l'exponent de x és el numerador #m.

]]> 4.02.2.117Q PotènciaFrac=arrel Escriu com a potència de #a el nombre #b:

#b = #a^{#1}

]]> 1.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>13</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>n</mi><mo>&lt;</mo><mi>d</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mi>n</mi><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mroot><msup><mi>a</mi><mi>n</mi></msup><mi>d</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>9</mn><mn>7</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> L'índex és el denominador de la fracció i la potència el numerador.

]]> 4.02.2.118Q Arrel=PotènciaFracc Escriu en forma d'arrel el nombre #a elevat a #b

]]> 1.0000000 0.5000000 0 0 #r_41 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>16</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>n</mi><mi>d</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_41</mi><mo>=</mo><mroot><msup><mi>a</mi><mi>n</mi></msup><mi>d</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_41</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>2</mn><mn>4</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_41</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> #n, el numerador, és l'exponent de #a.

#d, el denominador, és l'índex de l'arrel

]]> 4.02.2.130 TEORIA Introducció de factors Introducció de factors

Per introduir un factor es MULTIPLICA la seva potència per l'índex:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»12«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»14«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.130_1 TEORIA Introduir factors (GIF)

]]> 0.0000000 0.0000000 0 4.02.2.131Q Introduir factors arrel quadrada Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi»x«/mi»«mi»a«/mi»«/msup»«mo»§nbsp;«/mo»«mo»*«/mo»«mo»§nbsp;«/mo»«msup»«mi»y«/mi»«mi»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>*</mo><msqrt><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>x</mi><mn>9</mn></msup><mo>*</mo><msup><mi>y</mi><mn>8</mn></msup><mo>*</mo><msup><mi>z</mi><mn>4</mn></msup></mrow></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quan un factor entra sota l'arrel:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

Per exemple, l'exponent de x, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math» es transforma en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mstyle»«/math» quan x entra sota l'arrel, i després cal sumar («math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mstyle»«/math») que és l'exponent que té la x sota l'arrel, o sigui «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»c«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mstyle»«/math»

]]> 4.02.2.132Q Introduir factors arrel quadrada_2 Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi»x«/mi»«mi»a«/mi»«/msup»«mo»§nbsp;«/mo»«mo»*«/mo»«mo»§nbsp;«/mo»«msup»«mi»y«/mi»«mi»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi»n«/mi»«/mroot»«/math»

]]> 4.02.2.133Q Introduir factors arrel cúbica Introduïu tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi»x«/mi»«mi»a«/mi»«/msup»«mo»§nbsp;«/mo»«mo»*«/mo»«mo»§nbsp;«/mo»«msup»«mi»y«/mi»«mi»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow><mn>3</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>*</mo><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><msup><mi>x</mi><mn>13</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></mrow><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Quan un factor entra sota l'arrel:
a) el seu exponent queda multiplicat per 3
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 4.02.2.134Q Introduir factors arrel cúbica Introduïu tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi»x«/mi»«mi»a«/mi»«/msup»«mo»§nbsp;«/mo»«mo»*«/mo»«mo»§nbsp;«/mo»«msup»«mi»y«/mi»«mi»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi»n«/mi»«/mroot»«/math»

]]> 4.02.2.210 TEORIA Càlcul d'arrels Càlcul d'arrels

Per calcular una arrel,

es fa servir la calculadora per esbrinar si és exacta.
si no ho és es FACTORITZA el radicand i es treuen tots els factors possibles:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»13«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»500«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«msup»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»15«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»4«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.230 TEORIA Radicals semblants/Agrupar Radicals semblants/agrupar

Dos radicals són semblants si tenen el mateix índex i el mateix radicand. Es poden agrupar sumant els coeficients:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»7«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»6«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.230_1 TEORIA Suma i resta de radicals Suma i resta de radicals SEMBLANTS

Si són semblants, els radicals es poden sumar i restar, sumant i restant els seus coeficients.

]]> 0.0000000 0.0000000 0 4.02.2.230_2 TEORIA Agrupar radicals (GIF)

]]> 0.0000000 0.0000000 0 4.02.2.231 Agrupar radicals semblants Agrupa els radicals semblants en l'expressió:
#a_1 - #a_2 + #a_3 - #a_4
Pensa en posar els asteriscs en la resposta!

]]> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 + #c_3

Per #e_2, el coeficient és: #d_2 = -#c_2 - #c_4

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>-</mo><mi>a_2</mi><mo>+</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>+</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mo>-</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>20</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> 4.02.2.232 Agrupar radicals semblants_2 Agrupa els radicals semblants en l'expressió:
#a_1 + #a_2 - #a_3 - #a_4
Pensa en posar els asteriscs en la resposta!

]]> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 - #c_3

Per #e_2, el coeficient és: #d_2 = #c_2 - #c_4

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>a_2</mi><mo>-</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>-</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>4</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> 4.02.2.233Q Agrupar radicals semblants Agrupa els radicals semblants en l'expressió:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«/mrow»«/mstyle»«/math»
Pensa en posar els asteriscs en la resposta!

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>-</mo><mi>a_2</mi><mo>+</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>+</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mo>-</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>20</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 + #c_3

Per #e_2, el coeficient és: #d_2 = -#c_2 - #c_4

]]> 4.02.2.310 TEORIA Arrel d'un producte Producte de radicals semblants

El producte d'arrels de mateix índex és igual a l'arrel del producte

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo»§#183;«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»125«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo»=«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»625«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»5«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/math»

El resultat s'ha de simplificar sempre.

Si les arrels no tenen el mateix índex,

cal reduir-les a índex comú.

]]> 0.0000000 0.0000000 0 4.02.2.311Q Producte d'arrels (index 2) Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/mstyle»«/math»

]]> 4.02.2.312Q Producte d'arrels (index 3) Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mroot»«mn»5«/mn»«mn»3«/mn»«/mroot»«/math»

]]> 4.02.2.320 TEORIA Racionalització I Racionalització

Si una expressió té una arrel al denominador, cal eliminar-la. El cas més senzill és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»2«/mn»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.321Q Racionalització index 2 Racionalitza «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msqrt»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msqrt»«/mfrac»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«mn»3«/mn»«/mfrac»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msqrt><mi>a1</mi></msqrt></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msqrt><mi>b1</mi></msqrt></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>b1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>33</mn></msqrt><mn>11</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per racionalitzar, cal multiplicar el numerador i el denominador per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msqrt»«/mstyle»«/math»: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#003300¨»«mrow»«msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»#«/mo»«mi mathvariant=¨bold¨ mathsize=¨12px¨»a«/mi»«mn mathvariant=¨bold¨ mathsize=¨12px¨»1«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»§#183;«/mo»«msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»#«/mo»«mi mathvariant=¨bold¨ mathsize=¨12px¨»b«/mi»«mn mathvariant=¨bold¨ mathsize=¨12px¨»1«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»#«/mo»«mi mathvariant=¨bold¨ mathsize=¨12px¨»b«/mi»«mn mathvariant=¨bold¨ mathsize=¨12px¨»1«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»§#183;«/mo»«msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»#«/mo»«mi mathvariant=¨bold¨ mathsize=¨12px¨»b«/mi»«mn mathvariant=¨bold¨ mathsize=¨12px¨»1«/mn»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»=«/mo»«mfrac mathcolor=¨#003300¨»«msqrt»«mo mathvariant=¨bold¨ mathsize=¨12px¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathsize=¨12px¨»p«/mi»«/msqrt»«mrow»«mo mathvariant=¨bold¨ mathsize=¨12px¨»#«/mo»«mi mathvariant=¨bold¨ mathsize=¨12px¨»b«/mi»«mn mathvariant=¨bold¨ mathsize=¨12px¨»1«/mn»«/mrow»«/mfrac»«/math»

que cal simplificar si es pot

]]> 4.02.2.330 TEORIA Quocient d'arrels Quocient de radicals semblants

El quocient de dues arrels de mateix índex és igual a l'arrel del quocient de radicands «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mroot»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«mroot»«mn mathvariant=¨bold¨»7«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»7«/mn»«/mfrac»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«/mrow»«/mstyle»«/math»

El resultat s'ha de simplificar sempre.

]]> 0.0000000 0.0000000 0 4.02.2.331Q Quocient d'arrels (index 2) Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mfrac»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

També pot ser que calgui racionalitzar.

]]> 4.02.2.332Q Quocient d'arrels (index 3) Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mroot»«mn»3«/mn»«mn»3«/mn»«/mroot»«/math»

]]> 4.02.2.340 TEORIA Arrel d'una arrel Arrel d'una arrel

L'arrel n-èsima d'una arrel m-èsima és una arrel d'índex n·m.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mroot»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»m«/mi»«/mroot»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»nm«/mi»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.341Q Arrel d'una arrel Escriu com una sola arrel i simplifica si s'escau: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mroot»«/mstyle»«/math»

]]> 4.02.2.350 TEORIA Arrel d'una potència Potència d'una arrel

Per elevar una arrel, n'hi ha prou amb elevar el seu radicand

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mroot»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»5«/mn»«/mroot»«/mfenced»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mn mathvariant=¨bold¨»5«/mn»«/mroot»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.351Q Potència d'una arrel Eleva i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>49</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mroot><mi>a1</mi><mi>m1</mi></mroot></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>mcd</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>n1</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>a</mi><mi>n1</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>n1</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>sol</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mi>m1</mi><mi>k</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mfrac><mi>n1</mi><mi>k</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>n2</mi></msup><mi>m2</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>40</mn><mn>9</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>,</mo><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>40</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>,</mo><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>5</mn><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El resultat és del tipus «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/msup»«/mstyle»«/math»

Primer es simplifica la fracció: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

i després l'arrel: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mstyle»«/math»

]]> 4.02.2.360 TEORIA Simplificació Simplificació

Una arrel està simplificada quan:

l' índex i l'exponent són primers entre ells
ja no es pot treure cap factor
el radicand no és una fracció

]]> 0.0000000 0.0000000 0 4.02.2.360_1 TEORIA Extracció de factors Extracció de factors

Per extreure un factor, es DIVIDEIX la seva potència per l'índex (el quocient queda a fora, i el residu a dins):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»11«/mn»«/msup»«mn»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/math» (11: = 2 ·4 + 3)

També es pot fer així: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»11«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«/mrow»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.360_2 TEORIA Simplificar (GIF)

]]> 0.0000000 0.0000000 0 4.02.2.361Q Simplificar arrel quadrada Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«/msqrt»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»6«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #s <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>*</mo><msup><mn>3</mn><mi>b</mi></msup></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>r</mi><mo><</mo><mn>1000000</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>r</mi><mo>></mo><mn>100</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msqrt><mi>r</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>q1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>,</mo><mi>q2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>93312</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>216</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»
Fem les divisions enteres amb quocient i residu:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Per tant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»

"quocient a fora, residu a dins"

]]> 4.02.2.362Q Simplificar arrel quadrada_2 Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«/msqrt»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»6«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #s <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>*</mo><msup><mn>5</mn><mi>b</mi></msup></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>r</mi><mo><</mo><mn>1000000</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>r</mi><mo>></mo><mn>100</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msqrt><mi>r</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>q1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>,</mo><mi>q2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>93312</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>216</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/mstyle»«/math»
Fem les divisions enteres amb quocient i residu:

Per tant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«/mstyle»«/math»

"quocient a fora, residu a dins"

]]> 4.02.2.363Q Simplificar arrel quadrada_3 Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#00007F¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«/msqrt»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»6«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #s <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>r</mi><mo>=</mo><msup><mn>3</mn><mi>a</mi></msup><mo>*</mo><msup><mn>5</mn><mi>b</mi></msup></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>r</mi><mo><</mo><mn>10000</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>r</mi><mo>></mo><mn>100</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msqrt><mi>r</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>q1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>,</mo><mi>q2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>405</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/mstyle»«/math»
Fem les divisions enteres amb quocient i residu:

Per tant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«/mstyle»«/math»

"quocient a fora, residu a dins"

]]> 4.02.2.364Q Simplificar arrel cúbica Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»3«/mn»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_2</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>·</mo><msup><mn>3</mn><mi>b</mi></msup><mo>*</mo><mi>c</mi></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mroot><mi>r_2</mi><mn>3</mn></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>r_2</mi><mo><</mo><mn>10000</mn></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4032</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mroot><mn>63</mn><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».

Cal fer la divisió entera per 3 i treure el quocient fora i deixar el residu dins l'arrel.

]]> 4.02.2.370 TEORIA Radicals equivalents Radicals equivalents

Dos o més radicals són dits equivalents si els seus exponents fraccionaris són equivalents: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»5«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»12«/mn»«/msup»«mn mathvariant=¨bold¨»20«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»perqu§#232;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»5«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»12«/mn»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«/math»

Com que es tracta de fraccions, es poden simplificar, amplificar i existeix una fracció irreductible.

]]> 0.0000000 0.0000000 0 4.02.2.371Q Trobar radical equivalent Transforma l'arrel «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mroot»«/mstyle»«/math» en una arrel que tingui per índex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mo> </mo><mi>k</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>k</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mroot><msup><mi>x</mi><mi>m1</mi></msup><mi>n1</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>,</mo><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>,</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mi>x</mi><mn>25</mn></msup><mn>15</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que l'índex es multiplica per #k, cal multiplicar l'exponent de x per #k

]]> 4.02.2.372Q Simplifica arrel amb índex i exponent Simplifica l'arrel «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mroot»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mo> </mo><mi>k</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>k</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mroot><msup><mi>x</mi><mi>m</mi></msup><mi>n</mi></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>,</mo><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mi>x</mi><mn>2</mn></msup><mn>5</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'índex i l'exponent es poden dividir per #k

]]> 4.02.2.373Q Calcular radical equivalent Quin és el valor de m que fa certa la igualtat: #a_1 = #a_2?

Format de la resposta: m=4

]]> 4.02.2.374Q Calcular radical equivalent Quin és el valor de k que fa certa la igualtat: #a_1 = #a_2?

Format de la resposta: m=4

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>b1</mi></msup><mi>i_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>d</mi><mo>*</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>b2</mi></msup><mi>k</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>d</mi><mo>*</mo><mi>i_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msup><mi>c</mi><mi>b1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><msup><mi>c</mi><mi>b2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>4</mn><mn>5</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>1024</mn><mi>k</mi></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si els dos radicals són equivalents, cal que les fraccions que representen els seus exponents siguin equivalents.

Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mstyle»«/math» cal resoldre l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mi mathvariant=¨bold¨»k«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 4.02.2.380 TEORIA Reducció a índex comú Reducció a índex comú

Per reduir a índex comú, es fa com en les fraccions:

es calcula el mcm dels índex
s'escriuen fraccions equivalents amb aquest mcm de denominador.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»mcm«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8594;«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»9«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mn mathvariant=¨bold¨»7«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 4.02.2.481Q Calcular mínim comú índex Quin és el mínim comú índex dels radicals següents?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_13 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a_1</mi><mo>≠</mo><mi>a_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mroot><mn>2</mn><mi>a_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mroot><mn>2</mn><mi>a_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><msqrt><mn>2</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>r_13</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>15</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>210</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_13</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> És el mínim comú múltiple de 2, #a_1 i #a_2
Cal fer la descomposició en factors i agafar un factor de cada, amb els exponents més grans: #d

]]> 4.02.2.482Q Calcular mínim comú índex_2 Quin és el mínim comú índex dels radicals següents?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»b«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»b«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»b«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«/mrow»«/mstyle»«/math»

]]> 4.02.2.490 TEORIA Multiplicar radicals

]]> 0.0000000 0.0000000 0 4.02.2.491Q Radicals: reduïr a mcíndex i multiplicar Redueix a mínim comú índex i multiplica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»j«/mi»«/mrow»«/mroot»«/mrow»«/mstyle»«/math»

Format de la resposta: arrel simplificada

Després eleva els radicands #a_1 i #a_2 per tal que els radicals siguin equivalents.

]]> 4.02.2.492Q Radicals: reduïr a mcíndex i multiplicar Redueix a mínim comú índex i multiplica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»j«/mi»«/mrow»«/mroot»«/mrow»«/mstyle»«/math»

Format de la resposta: arrel simplificada

Després eleva els radicands #a_1 i #a_2 per tal que els radicals siguin equivalents.

]]> 4t ESO/4.02 POTÈNCIES I ARRELS/4.02.3 Potències d'exponent fraccionari 4.02.3.10 TEORIA. Arrel i pot. fraccionària Arrels i exponents fraccionaris L'arrel d'índex n d'un nombre sempre es pot escriure com aquest nombre elevat a un exponent de denominador n:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»p«/mi»«/msup»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathcolor=¨#00007F¨»§#160;«/mo»«mo mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mi mathvariant=¨bold¨»p«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mfrac»«/msup»«/math»
Exemple: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mn»81«/mn»«mn»5«/mn»«/mroot»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mroot»«msup»«mn»3«/mn»«mn»4«/mn»«/msup»«mn»5«/mn»«/mroot»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mn»3«/mn»«mfrac»«mn»4«/mn»«mn»5«/mn»«/mfrac»«/msup»«/math»

]]> 0.0000000 0.0000000 0 4.02.3.11Q Arrel i potència fraccionària Quin és l'exponent de #b en transformar en potència fraccionària l'expressió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»

Format de la resposta: 5/7

El numerador és la potència del nombre
El denominador és l'índex de l'arrel

Si es pot, simplifiquem la fracció.

]]> 4.02.3.21Q Arrel i potència fraccionària Quin és l'exponent de x en transformar en potència fraccionària l'expressió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»

Format de la resposta: 5/7

El numerador és la potència del nombre
El denominador és l'índex de l'arrel

Si es pot, simplifiquem la fracció.

]]> 4.02.3.31Q De potència fraccionària a arrel Escriu en forma d'arrel simplificada la potència fraccionària: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mfrac»«/msup»«/mstyle»«/math»

]]> 4.02.3.50 TEORIA: Operar amb pot. fraccion. Operacions amb exponents fraccionaris Multiplicació:
Sumem els exponents (cal calcular el mcm dels denominadors)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»5«/mn»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/msup»«mo»§nbsp;«/mo»«mo»·«/mo»«mo»§nbsp;«/mo»«msup»«mn»5«/mn»«mfrac»«mn»2«/mn»«mn»5«/mn»«/mfrac»«/msup»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mn»5«/mn»«mrow»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mn»2«/mn»«mn»5«/mn»«/mfrac»«/mrow»«/msup»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«msup»«mn»5«/mn»«mfrac»«mn»23«/mn»«mn»20«/mn»«/mfrac»«/msup»«/math»

Divisió:
Restem els exponents (cal calcular el mcm dels denominadors)«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»5«/mn»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/msup»«mo»§nbsp;«/mo»«mo»:«/mo»«mo»§nbsp;«/mo»«msup»«mn»5«/mn»«mfrac»«mn»2«/mn»«mn»5«/mn»«/mfrac»«/msup»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mn»5«/mn»«mrow»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mn»2«/mn»«mn»5«/mn»«/mfrac»«/mrow»«/msup»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mn»5«/mn»«mfrac»«mn»7«/mn»«mn»20«/mn»«/mfrac»«/msup»«/math»

Igual que amb les arrels, no es poden sumar ni restar, només es poden AGRUPAR

]]> 0.0000000 0.0000000 0 4.02.3.51Q Operacions amb exponent fraccionari Amb les potències fraccionàries: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»j«/mi»«/mrow»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«/mstyle»«/math», calcula:

a) a · b

b) a/b

Format de la resposta: arrel simplificada

]]> 1.0000000 0.5000000 0 0 a) = #sol1b) =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>p</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>j</mi><mo>,</mo><mi>q</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>i</mi><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>p</mi><mo>≠</mo><mi>q</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mi>x</mi><mrow><mfrac><mi>p</mi><mi>i</mi></mfrac><mo>+</mo><mfrac><mi>q</mi><mi>j</mi></mfrac></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><mi>x</mi><mrow><mfrac><mi>p</mi><mi>i</mi></mfrac><mo>-</mo><mfrac><mi>q</mi><mi>j</mi></mfrac></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>i</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>j</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><msup><mroot><mi>x</mi><mn>21</mn></mroot><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mroot><mi>x</mi><mn>21</mn></mroot><mn>5</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a) Cal sumar les fraccions

b) Cal restar la segona fracció de la primera

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