Answer
$\frac{\sqrt[4] y}{3x}$
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, $\sqrt[4] (\frac{y}{81x^{4}})=\frac{\sqrt[4] y}{\sqrt[4] (81x^{4})}=\frac{\sqrt[4] y}{3x}$
We know that $\sqrt[4] (81x^{4})=3x$, because $(3x)^{4}=(3\times3\times3\times3)\times x^{1+1+1+1}=81x^{4}$