Simplify cube root of -3125xy^3

$\sqrt[3]{- 3125 x y^{3}}$

Step 1

Rewrite $- 3125 x y^{3}$ as ${(- 5 y)}^{3} \cdot (25 x)$ .

Factor $- 125$ out of $- 3125$ .

$\sqrt[3]{- 125 (25) x y^{3}}$

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

$\sqrt[3]{{(- 5)}^{3} \cdot 25 x y^{3}}$

Move $x$ .

$\sqrt[3]{{(- 5)}^{3} \cdot 25 y^{3} x}$

Move $25$ .

$\sqrt[3]{{(- 5)}^{3} y^{3} \cdot 25 x}$

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

$\sqrt[3]{{(- 5 y)}^{3} \cdot 25 x}$

Add parentheses.

$\sqrt[3]{{(- 5 y)}^{3} \cdot (25 x)}$

Step 2

Pull terms out from under the radical.

$- 5 y \sqrt[3]{25 x}$