Simplify cube root of -125x^2y^4

$\sqrt[3]{- 125 x^{2} y^{4}}$

Step 1

Rewrite $- 125 x^{2} y^{4}$ as ${(- 5 y)}^{3} (x^{2} y)$ .

Rewrite $- 125$ as ${(- 5)}^{3}$ .

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

Factor out $y^{3}$ .

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

Move $x^{2}$ .

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

Rewrite ${(- 5)}^{3} y^{3}$ as ${(- 5 y)}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$- 5 y \sqrt[3]{x^{2} y}$