Answer
$\frac{\sqrt[4] (a^{3})}{3}$
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, $\sqrt[4] (\frac{a^{3}}{81})=\frac{\sqrt[4] (a^{3})}{\sqrt[4] 81}=\frac{\sqrt[4] (a^{3})}{3}$
We know that $\sqrt[4] 81=3$, because $3^{4}=81$.