Simplify fourth root of y/(81x^4)

$\sqrt[4]{\frac{y}{81 x^{4}}}$

Rewrite $\frac{y}{81 x^{4}}$ as ${(\frac{1}{3 x})}^{4} y$ .

Factor the perfect power $1^{4}$ out of $y$ .

$\sqrt[4]{\frac{1^{4} y}{81 x^{4}}}$

Factor the perfect power ${(3 x)}^{4}$ out of $81 x^{4}$ .

$\sqrt[4]{\frac{1^{4} y}{{(3 x)}^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} y}{{(3 x)}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{3 x})}^{4} y}$

Pull terms out from under the radical.

$\frac{1}{3 x} \sqrt[4]{y}$

Combine $\frac{1}{3 x}$ and $\sqrt[4]{y}$ .

$\frac{\sqrt[4]{y}}{3 x}$