Simplify cube root of -81x^6y^5

$\sqrt[3]{- 81 x^{6} y^{5}}$

Step 1

Rewrite $- 81 x^{6} y^{5}$ as ${(- 3 x^{2} y)}^{3} \cdot (3 y^{2})$ .

Factor $- 27$ out of $- 81$ .

$\sqrt[3]{- 27 (3) x^{6} y^{5}}$

Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

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

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

Factor out $y^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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