Answer
$\frac{\sqrt[4] 8}{x^{2}}$
Work Step by Step
The quotient rule holds that $\sqrt[n] (\frac{a}{b})=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero).
Therefore, $\sqrt[4] (\frac{8}{x^{8}})=\frac{\sqrt[4] 8}{\sqrt[4] (x^{8})}=\frac{\sqrt[4] 8}{x^{2}}$
We know that $\sqrt[4] (x^{8})=x^{2}$, because $(x^{2})^{4}=x^{2\times4}=x^{8}$.
