Simplify cube root of -192x^6y^4

$\sqrt[3]{- 192 x^{6} y^{4}}$

Step 1

Rewrite $- 192 x^{6} y^{4}$ as ${(- 4 x^{2} y)}^{3} \cdot (3 y)$ .

Factor $- 64$ out of $- 192$ .

$\sqrt[3]{- 64 (3) x^{6} y^{4}}$

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

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

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

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

Factor out $y^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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