Answer
$\frac{2}{y^{4}}$
Work Step by Step
he quotient rule for radicals tells us that $\sqrt[n]\frac{a}{b}=\frac{\sqrt[n]a}{\sqrt[n]b}$ (if $\sqrt[n]a$ and $\sqrt[n]b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots.
Therefore, $\sqrt[5]\frac{32}{y^{20}}=\frac{\sqrt[5]32}{\sqrt[5]y^{20}}=\frac{2}{y^{4}}$.
$\sqrt[5] 32=2$, because $2^{5}=32$
$\sqrt[5] y^{20}=y^{4}$, because $(y^{4})^{5}=y^{4\times5}=y^{20}$
