Question

Pergunta anexa (foto).

Answer 1

$Resolu\c{c}\~ao\to \left\{\begin{array}{ccc} \sqrt[4]{5}* \sqrt{5}* \sqrt[4]{5}* \sqrt[3]{5} = \\\\ \sqrt[4]{5*5}* \sqrt{5}* \sqrt[3]{5}=\\\\ \sqrt[4]{5^2}* \sqrt{5}* \sqrt[3]{5}= \\\\ 5^{ \frac{2}{4}}*5^{ \frac{1}{2} } * 5^{ \frac{1}{3} } = \\\\5^{ \frac{2}{4} + \frac{1}{2}+ \frac{1}{3} } = 5^{ \frac{6+6+4}{12} } = 5^{ \frac{16}{12} }= \\\\\boxed{\boxed{5^{ \frac{4}{3} } = \sqrt[3]{5^3*5} = 5 \sqrt[3]{5} }}\to Letra\ B \end{array}\right$

Espero ter ajudado. :))

Answer 2

$\sqrt[4]{5} = 5^{ \frac{1}{4} } => 5^{ \frac{3}{12} } \\\\ \sqrt[2]{5} = 5^{ \frac{1}{2} } => 5^{ \frac{6}{12} }\\\\ \sqrt[4]{5} = 5^{ \frac{1}{4} } => 5^{ \frac{3}{12} }\\\\ \sqrt[3]{5} = 5^{ \frac{1}{3} } => 5^{ \frac{4}{12} }\\\\ \sqrt[4]{5}. \sqrt[2]{5}. \sqrt[4]{5}. \sqrt[3]{5} = 5^{ \frac{3}{12} }.5^{ \frac{6}{12} }.5^{ \frac{3}{12} }.5^{ \frac{4}{12} }\\\\ 5^{ \frac{16}{12} } = 5^{ \frac{4}{3} } = > \sqrt[3]{ 5^{4} } => \boxed{\boxed{ 5\sqrt[3]{5} }}$