Question

qual das opções esta incorreta?
a) ³√3= ¹²√3^4
b)^6√8³ =³√8
c)^5√6^4=^10√6^8
d)^4√6^6 =6
e)^6√5² =³√5

Answer 1

Olá Igor,


$a)~\sqrt[3]{3}=\sqrt[12]{3^4}\\3^\frac{1}{3}=3^{\frac{\not{4}}{\not{12}}}\\3^\frac{1}{3}=3^\frac{1}{3}~\gets~\mathsf{correto}\\\\b)~\sqrt[6]{8^3}=\sqrt[3]{8}\\8^\frac{\not{3}}{\not{6}}=8^\frac{1}{3}\\8^\frac{1}{2} \neq 8^\frac{1}{3}~\gets~\mathsf{incorreto}\\\\c)~\sqrt[5]{6^4}=\sqrt[10]{6^8}\\6^\frac{4}{5}=6^\frac{\not{8}}{\not{10}}\\6^\frac{4}{5}=6^\frac{4}{5}~\gets~\mathsf{correto}$

$d)~\sqrt[4]{6^6}=6\\6^\frac{\not{4}}{\not{6}}=6\\6^\frac{2}{3} \neq 6~\gets~\mathsf{incorreto}\\\\e)~\sqrt[6]{5^2}=\sqrt[3]{5}$
$5^\frac{\not{2}}{\not{6}}=5^\frac{1}{3}\\5^\frac{1}{3}=5^\frac{1}{3}~\gets~\mathsf{correto}$


Dúvidas? comente