Simplify fourth root of x^8y^7

$\sqrt[4]{x^{8} y^{7}}$

Step 1

Rewrite $x^{8} y^{7}$ as ${(x^{2} y)}^{4} y^{3}$ .

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

$\sqrt[4]{{(x^{2})}^{4} y^{7}}$

Factor out $y^{4}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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