POTÈNCIA D'EXPONENT POSITIU |
Expressen un producte reiterat:
35 = 3·3·3·3·3 = 243
Si es calcula la potència d'un nombre negatiu:
A la calculadora, per exponents superiors a 2, es fan servir les tecles: shift ×(multiplicat); ^ ; x■ |
]]>
NO ET DEIXIS ELS PARÈNTESIS
Quan la potència és parella, el resultat sempre és positiu.
]]>NO ET DEIXIS ELS PARÈNTESIS
La potència imparella d'un nombre negatiu és negativa.
]]>NO ET DEIXIS ELS PARÈNTESIS
#t
]]>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»
|
]]>
«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
]]>«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»
]]>
«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»
]]>«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»
]]>
«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»
]]>«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»
]]>
«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»
]]>Productes de potències |
Per multiplicar potències de la mateixa base,
cal SUMAR els exponent:
35 · 38 = 31339 · 3-11 = 3-2 |
]]>
]]>
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» |
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»
]]>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»
]]>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» |
Format de la resposta: Enter o fracció
]]>Escriviu el resultat com una potència
Escriviu el resultat com una potència
S'anomena arrel n-èsima del nombre x, el nombre y que elevat a n dona x: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»y«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«/math»
També es pot escriure com un exponent FRACCIONARI:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msup»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfrac»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mfrac»«/msup»«/math»
]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»
]]>]]>
]]>
]]>
]]>
Format: escriu només l'exponent, no la x.
]]>#d, el denominador, és l'índex de l'arrel
]]>Per introduir un factor es MULTIPLICA la seva potència per l'índex:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»12«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»14«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/math»
Per exemple, l'exponent de x, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math» es transforma en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mstyle»«/math» quan x entra sota l'arrel, i després cal sumar («math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mstyle»«/math») que és l'exponent que té la x sota l'arrel, o sigui «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»c«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mstyle»«/math»
]]>
Per exemple, l'exponent de x, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math» es transforma en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«/mrow»«/mstyle»«/math» quan x entra sota l'arrel, i després cal sumar («math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mstyle»«/math») que és l'exponent que té la x sota l'arrel, o sigui «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»c«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mstyle»«/math»
]]>
Per calcular una arrel,
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»13«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»500«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«msup»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»15«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»4«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/math»
Dos radicals són semblants si tenen el mateix índex i el mateix radicand. Es poden agrupar sumant els coeficients:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»7«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»6«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/math»
Si són semblants, els radicals es poden sumar i restar, sumant i restant els seus coeficients.
El producte d'arrels de mateix índex és igual a l'arrel del producte
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo»§#183;«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»125«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo»=«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»625«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»5«/mn»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/math»
El resultat s'ha de simplificar sempre.
Si les arrels no tenen el mateix índex,
cal reduir-les a índex comú.
Si una expressió té una arrel al denominador, cal eliminar-la. El cas més senzill és:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»2«/mn»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/math»
que cal simplificar si es pot
]]>
El quocient de dues arrels de mateix índex és igual a l'arrel del quocient de radicands «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mroot»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«mroot»«mn mathvariant=¨bold¨»7«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»7«/mn»«/mfrac»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«/mrow»«/mstyle»«/math»
El resultat s'ha de simplificar sempre.
També pot ser que calgui racionalitzar.
]]>
L'arrel n-èsima d'una arrel m-èsima és una arrel d'índex n·m.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«mroot»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»m«/mi»«/mroot»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»nm«/mi»«/mroot»«/math»
Per elevar una arrel, n'hi ha prou amb elevar el seu radicand
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mroot»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»5«/mn»«/mroot»«/mfenced»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mn mathvariant=¨bold¨»5«/mn»«/mroot»«/mrow»«/mstyle»«/math»
Primer es simplifica la fracció: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»
i després l'arrel: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mstyle»«/math»
]]>Una arrel està simplificada quan:
Per extreure un factor, es DIVIDEIX la seva potència per l'índex (el quocient queda a fora, i el residu a dins):
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»11«/mn»«/msup»«mn»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/math» (11: = 2 ·4 + 3)
També es pot fer així: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»11«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«/mrow»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/math»
Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»6«/mn»«/msqrt»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Per tant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»
"quocient a fora, residu a dins"
]]>Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»6«/mn»«/msqrt»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Per tant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«/mstyle»«/math»
"quocient a fora, residu a dins"
]]>Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»6«/mn»«/msqrt»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»
Per tant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/msqrt»«/mstyle»«/math»
"quocient a fora, residu a dins"
]]>Cal fer la divisió entera per 3 i treure el quocient fora i deixar el residu dins l'arrel.
Dos o més radicals són dits equivalents si els seus exponents fraccionaris són equivalents: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»5«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»12«/mn»«/msup»«mn mathvariant=¨bold¨»20«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»perqu§#232;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»5«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»12«/mn»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«/math»
Com que es tracta de fraccions, es poden simplificar, amplificar i existeix una fracció irreductible.
]]>
Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mstyle»«/math» cal resoldre l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mi mathvariant=¨bold¨»k«/mi»«/mfrac»«/mrow»«/mstyle»«/math»
Per reduir a índex comú, es fa com en les fraccions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»mcm«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8594;«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mroot mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»9«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mroot mathcolor=¨#00007F¨»«msup»«mn mathvariant=¨bold¨»7«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«/math»
Després eleva els radicands #a_1 i #a_2 per tal que els radicals siguin equivalents.
]]>Després eleva els radicands #a_1 i #a_2 per tal que els radicals siguin equivalents.
]]>Format de la resposta: 5/7
]]>Si es pot, simplifiquem la fracció.
]]>Format de la resposta: 5/7
]]>Si es pot, simplifiquem la fracció.
]]>a) a · b
b) a/b
Format de la resposta: arrel simplificada
]]>b) Cal restar la segona fracció de la primera
]]>