Question

aplicando as propriedades das potencias calcule o valor das expressoes

Answer 1

A (a) está um pouco dificil pra entender, portanto, se eu tiver escrito a expressão original errada, deixe um comentário para que eu possa corrigir.

Antes de começar, vamos recordar as tres propriedades que são utilizadas nesta questão:

$\rightarrow~\left(b^a\right)^c~=~b^{\,a\,.\,c}~=~b^{ac}\\\\\rightarrow~b^a~.~b^c~=~b^{a+c}\\\\\rightarrow~\frac{b^a}{b^c}=b^{a-c}$

a)

$\left[\left(-4\right)^7.\left(-4\right)^{10}.\left(-4\right)\right]:\left[\left(-4\right)^8\right]^2\\\\\\\frac{\left[\left(-4\right)^7.\left(-4\right)^{10}.\left(-4\right)\right]}{\left[\left(-4\right)^8\right]^2}\\\\\\\frac{\left(-4\right)^{7+10+1}}{\left(-4\right)^{\,8\,.\,2}}\\\\\\\frac{\left(-4\right)^{18}}{\left(-4\right)^{16}}\\\\\\(-4)^{\,18-16}\\\\\\(-4)^2\\\\\\\boxed{16}$

b)

$\left[\left(-2\right)^6\right]^2:\left[\left(-2\right)^6.\left(-2\right)^{2}.\left(-2\right)\right]\\\\\\\frac{\left[\left(-2\right)^6\right]^2}{\left[\left(-2\right)^6.\left(-2\right)^{2}.\left(-2\right)\right]}\\\\\\\frac{\left(-2\right)^{\,6\,.\,2}}{\left(-2\right)^{6+2+1}}\\\\\\\frac{\left(-2\right)^{12}}{\left(-2\right)^{9}}\\\\\\(-2)^{12-9}\\\\\\(-2)^3\\\\\\\boxed{-8}$