Question

simplifique cada uma das expressões apresentadas a seguir:
a)³√32•2^-⅔•(⅔)^0
b)4^10•8^-3•-2 elevado a 32

Answer 1

Olá.

a)

$( \sqrt[3]{32}).(2^{-\frac{2}{3}}).(\frac{2}{3})^0\\\\ (\sqrt[3]{2^3.2}).(2^{-\frac{2}{3}}).1\\\\ 2.(\sqrt[3]{2}).(2^{-\frac{2}{3}})\\\\ 2^1.2^{\frac{1}{3}}.2^{-\frac{2}{3}} \longrightarrow 1+\frac{1}{3}-\frac{2}{3}} = \frac{3+1-2}{3} = \frac{2}{3}\\\\ 2^{\frac{2}{3}}$

b)

$\frac{4^{10}.8^{-3}.(-2)}{32} \\\\ \longrightarrow 4 = 2^2\\ \longrightarrow 8 = 2^3\\ \longrightarrow 32 = 2^5\\\\ \frac{(2^2)^{10}.(2^3)^{-3}.(-2)}{2^5}\\\\ \frac{2^{20}.2^{-9}.(-2)}{2^5}\\\\ \frac{2^{11}.(-2)}{2^5}\\\\ 2^{11-5}.(-2)\\\\ 2^{6}.(-2^1)\\\\ (-2)^7$

Espero ter ajudado. Qualquer dúvida comenta aí.