Simplify cube root of -54x^9y^3

$\sqrt[3]{- 54 x^{9} y^{3}}$

Step 1

Rewrite $- 54 x^{9} y^{3}$ as ${(- 3 x^{3} y)}^{3} \cdot 2$ .

Factor $- 27$ out of $- 54$ .

$\sqrt[3]{- 27 (2) x^{9} y^{3}}$

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

$\sqrt[3]{{(- 3)}^{3} \cdot 2 x^{9} y^{3}}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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