Question

Potenciação. Alguem poderia me ajudar no passo a passo desse calculo?

Answer 1

.
$( \frac{x^{3+2+5}}{x^{5+10}} )^2= \\ \\ ( \frac{x^{10}}{x^{15}} )^2= \\ \\ ( \frac{1}{x^5} )^2= \frac{1}{x^{10}}$

Answer 2

AE mano,

use as propriedades da exponenciação..

$a^{0}=1\\\\ a^{m}\cdot a^{n}=a^{m+n}\\\\ a^{m}: a^{n}=a^{m-n}\\\\ (a^m)^n=a^{m\cdot n}$

aí vc vai entender melhor..

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$\left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^{3+2}\not x^5}{\not x^5\cdot x^{10}}\right)^2\\\\\\ \Rightarrow \left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^5}{x^{10}}\right)^2~~(divida~x^5~e~x^{10}~por~x^5)\\\\\\ \Rightarrow \left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^5\div x^5}{x^{10}\div x^5}\right)^2$

$\Rightarrow \left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^{5-5}}{x^{10-5}}\right)^2\\\\\\ \Rightarrow \left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^0}{x^5}\right)^2\\\\\\ \Rightarrow \left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^0}{x^5}\right)^2$

$\Rightarrow \left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{x^{0\cdot2}}{x^{5\cdot2}}\right)\\\\\\ \Rightarrow \Large\boxed{\left( \dfrac{x^3\cdot x^2\cdot x^5}{x^5\cdot x^{10}} \right)^2=\left( \dfrac{1}{x^{10}}\right)}$