Simplify cube root of -256x^2y^3

$\sqrt[3]{- 256 x^{2} y^{3}}$

Step 1

Rewrite $- 256 x^{2} y^{3}$ as ${(- 4 y)}^{3} \cdot (4 x^{2})$ .

Factor $- 64$ out of $- 256$ .

$\sqrt[3]{- 64 (4) x^{2} y^{3}}$

Rewrite $- 64$ as ${(- 4)}^{3}$ .

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

Move $x^{2}$ .

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

Move $4$ .

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

Rewrite ${(- 4)}^{3} y^{3}$ as ${(- 4 y)}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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