Simplify fourth root of (xy^6)/81

$\sqrt[4]{\frac{x y^{6}}{81}}$

Step 1

Rewrite $\frac{x y^{6}}{81}$ as ${(\frac{y}{3})}^{4} (x y^{2})$ .

Factor the perfect power $y^{4}$ out of $x y^{6}$ .

$\sqrt[4]{\frac{y^{4} (x y^{2})}{81}}$

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

$\sqrt[4]{\frac{y^{4} (x y^{2})}{3^{4} \cdot 1}}$

Rearrange the fraction $\frac{y^{4} (x y^{2})}{3^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{y}{3})}^{4} (x y^{2})}$

Step 2

Pull terms out from under the radical.

$\frac{y}{3} \sqrt[4]{x y^{2}}$

Step 3

Combine $\frac{y}{3}$ and $\sqrt[4]{x y^{2}}$ .

$\frac{y \sqrt[4]{x y^{2}}}{3}$