Simplify cube root of -375x^6y^4

$\sqrt[3]{- 375 x^{6} y^{4}}$

Step 1

Rewrite $- 375 x^{6} y^{4}$ as ${(- 5 x^{2} y)}^{3} \cdot (3 y)$ .

Factor $- 125$ out of $- 375$ .

$\sqrt[3]{- 125 (3) x^{6} y^{4}}$

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

$\sqrt[3]{{(- 5)}^{3} \cdot 3 x^{6} y^{4}}$

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

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

Factor out $y^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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