Simplify cube root of 512x^4y^5

$\sqrt[3]{512 x^{4} y^{5}}$

Step 1

Rewrite $512 x^{4} y^{5}$ as ${(8 x y)}^{3} (x y^{2})$ .

Rewrite $512$ as $8^{3}$ .

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

Factor out $x^{3}$ .

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

Factor out $y^{3}$ .

$\sqrt[3]{8^{3} (x^{3} x) (y^{3} y^{2})}$

Move $x$ .

$\sqrt[3]{8^{3} x^{3} y^{3} x y^{2}}$

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

$\sqrt[3]{{(8 x y)}^{3} x y^{2}}$

Add parentheses.

$\sqrt[3]{{(8 x y)}^{3} (x y^{2})}$

Step 2

Pull terms out from under the radical.

$8 x y \sqrt[3]{x y^{2}}$