Question

Simplifique os radicais:
a)
$\sqrt[3]{ {7}^{3} }$
b)
$\sqrt[6]{ {4}^{8} }$
c)
$\sqrt[5]{ {4}^{5} }$
d)
$\sqrt[12]{ {20}^{15} }$
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Answer 1

Lembrando que radicais podem ser escritos como expoentes fracionários, temos:

$\rightarrow~\sqrt[b]{a^c}~=~a^{\frac{c}{b}}$

$a)\\\\\sqrt[3]{7^3}~=~7^{\frac{3}{3}}~=~7^1~=~\boxed{7}\\\\\\b)\\\\\sqrt[6]{4^8}~=~4^{\frac{8}{6}}~=~4^{\frac{4}{3}}~=~\boxed{\sqrt[3]{4^4}~~ou~~\sqrt[3]{256}}\\\\\\c)\\\\\sqrt[5]{4^5}~=~4^{\frac{5}{5}}~=~4^1~=~\boxed{4}\\\\\\d)\\\\\sqrt[12]{20^{15}}~=~20^{\frac{15}{12}}~=~20^{\frac{5}{4}}~=~\boxed{\sqrt[4]{20^5}~~~ou~~~\sqrt[4]{3200000}}$