Answer
$\frac{1}{x^{3}}$
Work Step by Step
The 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, $\sqrt[5] \frac{1}{x^{15}}=\frac{\sqrt[5] 1}{\sqrt[5] x^{15}}=\frac{1}{x^{3}}$.
$\sqrt[5] 1=1$, because $1^{5}=1$
$\sqrt[5] x^{15}=x^{3}$, because $(x^{3})^{5}=x^{3\times5}=x^{15}$
