Simplify cube root of -16x^2y^3

$\sqrt[3]{- 16 x^{2} y^{3}}$

Step 1

Rewrite $- 16 x^{2} y^{3}$ as ${(- 2 y)}^{3} \cdot (2 x^{2})$ .

Factor $- 8$ out of $- 16$ .

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

Rewrite $- 8$ as ${(- 2)}^{3}$ .

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

Move $x^{2}$ .

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

Move $2$ .

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

Rewrite ${(- 2)}^{3} y^{3}$ as ${(- 2 y)}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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