Simplify cube root of 1000x^4y^5

$\sqrt[3]{1000 x^{4} y^{5}}$

Step 1

Rewrite $1000 x^{4} y^{5}$ as ${(10 x y)}^{3} (x y^{2})$ .

Rewrite $1000$ as $10^{3}$ .

$\sqrt[3]{10^{3} x^{4} y^{5}}$

Factor out $x^{3}$ .

$\sqrt[3]{10^{3} (x^{3} x) y^{5}}$

Factor out $y^{3}$ .

$\sqrt[3]{10^{3} (x^{3} x) (y^{3} y^{2})}$

Move $x$ .

$\sqrt[3]{10^{3} (x^{3}) y^{3} x y^{2}}$

Rewrite $10^{3} (x^{3}) y^{3}$ as ${(10 x y)}^{3}$ .

$\sqrt[3]{{(10 x y)}^{3} x y^{2}}$

Add parentheses.

$\sqrt[3]{{(10 x y)}^{3} (x y^{2})}$

Step 2

Pull terms out from under the radical.

$10 x y \sqrt[3]{x y^{2}}$