Simplify fourth root of 81x^8y^5

$\sqrt[4]{81 x^{8} y^{5}}$

Step 1

Rewrite $81 x^{8} y^{5}$ as ${(3 x^{2} y)}^{4} y$ .

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} x^{8} y^{5}}$

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

$\sqrt[4]{3^{4} {(x^{2})}^{4} y^{5}}$

Factor out $y^{4}$ .

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

Rewrite $3^{4} {(x^{2})}^{4} y^{4}$ as ${(3 x^{2} y)}^{4}$ .

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

Step 2

Pull terms out from under the radical.

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