Question

Reduza a uma potência de base 5: 1/125^2

Answer 1

Olá.

$\mathsf{5:\dfrac{1}{125^2}}\\\\\\ \mathsf{Vamos~fatorar~o~125~e~substituir~na~fra\c{c}\~ao.}\\\\\begin{array}{cccc}125&|&5\\25&|&5\\5&|&5\\1&|&=&5^3\end{array}\\\\\\ \mathsf{5:\dfrac{1}{125^2}=}\\\\ \mathsf{5:\dfrac{1}{(5^3)^2}=}\\\\ \mathsf{5:\dfrac{1}{5^6}=}\\\\ \mathsf{5\cdot\dfrac{5^6}{1}=}\\\\ \mathsf{5\cdot5^6=}\\\\ \mathsf{5^{1+6}=}\\\\ \boxed{\mathsf{5^{7}}}$

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Bons estudos.