Simplify fourth root of 16x^2y^7

$\sqrt[4]{16 x^{2} y^{7}}$

Step 1

Rewrite $16 x^{2} y^{7}$ as ${(2 y)}^{4} (x^{2} y^{3})$ .

Rewrite $16$ as $2^{4}$ .

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

Factor out $y^{4}$ .

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

Move $x^{2}$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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