Simplify cube root of -32xy^3

$\sqrt[3]{- 32 x y^{3}}$

Step 1

Rewrite $- 32 x y^{3}$ as ${(- 2 y)}^{3} \cdot (4 x)$ .

Factor $- 8$ out of $- 32$ .

$\sqrt[3]{- 8 (4) x y^{3}}$

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

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

Move $x$ .

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

Move $4$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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