Question

\frac{4}{\sqrt[5]{16}}
paso a paso porfis

Answer 1

Respuesta:

$\frac{4}{\sqrt[5]{16}}=2\sqrt[5]{2}$

Explicación paso a paso:

$\frac{4}{\sqrt[5]{16}}\\=\frac{4}{\sqrt[5]{4^2}}\\=\frac{4}{4^\frac{2}{5}}\\=4^{1-\frac{2}{5}}\\=4^{\frac{5}{5}-\frac{2}{5}}\\=4^{\frac{3}{5}}\\={\sqrt[5]{4^3}\\=\sqrt[5]{64}\\={\sqrt[5]{32\cdot 2}\\={\sqrt[5]{32}\cdot {\sqrt[5]{2}\\=2\cdot {\sqrt[5]{2}\\=2{\sqrt[5]{2}$