Question

determine o valor das potências ​

Answer 1

Explicação passo-a-passo:

Lembre-se que $\sf a^{\frac{b}{c}}=\sqrt[c]{a^b}$

a)

$\sf 8^{\frac{4}{3}}=\sqrt[3]{8^4}$

$\sf 8^{\frac{4}{3}}=\sqrt[3]{(2^3)^4}$

$\sf 8^{\frac{4}{3}}=\sqrt[3]{(2^4)^3}$

$\sf 8^{\frac{4}{3}}=2^4$

$\sf 8^{\frac{4}{3}}=\red{16}$

b)

$\sf 64^{\frac{3}{2}}=\sqrt[2]{64^3}$

$\sf 64^{\frac{3}{2}}=\sqrt[2]{(8^2)^3}$

$\sf 64^{\frac{3}{2}}=\sqrt[2]{(8^3)^2}$

$\sf 64^{\frac{3}{2}}=8^3$

$\sf 64^{\frac{3}{2}}=\red{512}$

c)

$\sf 16^{\frac{1}{4}}=\sqrt[4]{16^1}$

$\sf 16^{\frac{1}{4}}=\sqrt[4]{16}$

$\sf 16^{\frac{1}{4}}=\sqrt[4]{2^4}$

$\sf 16^{\frac{1}{4}}=\red{2}$