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

]]> 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>3</mn><mo>,</mo><mn>11</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</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>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>e</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow><mrow><mi>t</mi><mo>=</mo><mo>"</mo><mi>La</mi><mo> </mo><mi>potència</mi><mo> </mo><mi>parella</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>nombre</mi><mo> </mo><mi>sempre</mi><mo> </mo><mi>és</mi><mo> </mo><mi>positiva</mi><mo>"</mo></mrow><mrow><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></mrow></apply></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>6</mn><mo>,</mo><mo>-</mo><mn>6</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>46656</mn></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>parella</ms><mo> </mo><ms>d'un</ms><mo> </mo><ms>nombre</ms><mo> </mo><ms>sempre</ms><mo> </mo><ms>és</ms><mo> </mo><ms>positiva</ms></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">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es fa amb la calculadora amb les tecles indicades:

( #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»

]]>

]]> 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 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>&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>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>x</mi><mi>m</mi></msup><mo>·</mo><msup><mi>x</mi><mi>n</mi></msup></mrow><mrow><msup><mi>x</mi><mi>p</mi></msup><mo>*</mo><msup><mi>x</mi><mi>o</mi></msup></mrow></mfrac></mfenced><mi>q</mi></msup></math></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"><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><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"><mfrac><msup><mi>x</mi><mn>4</mn></msup><mn>1</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">#r_1</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question>
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 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>k</mi><mo>+</mo><mi>n</mi><mo>-</mo><mi>s_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_4</mi><mo>=</mo><mi>s_3</mi><mo>*</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_5</mi><mo>=</mo><mfenced><mrow><mfenced><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mi>p</mi><mo>+</mo><mi>o</mi></mrow></mfenced></mrow></mfenced><mo>*</mo><mi>q</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_5</mi><mo>≠</mo><mn>0</mn></mrow><mrow><mi>j</mi><mo>=</mo><mo>&quot;</mo><mo> </mo><mo>&quot;</mo></mrow><mrow><mi>j</mi><mo>=</mo><mo>&quot;</mo><mo>(</mo><mn>1</mn><mo>=</mo><msup><mi>x</mi><mn>0</mn></msup><mo>)</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi><mo>=</mo><msup><mfenced><mfrac><mrow><msup><mi>x</mi><mi>m</mi></msup><mo>·</mo><msup><mi>x</mi><mi>n</mi></msup></mrow><mrow><msup><mi>x</mi><mi>p</mi></msup><mo>*</mo><msup><mi>x</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"><mi>r_1</mi><mo>=</mo><mi>m</mi></math></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>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 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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}

]]> 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><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

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