Simplify cube root of -162x^8

$\sqrt[3]{- 162 x^{8}}$

Step 1

Rewrite $- 162 x^{8}$ as ${(- 3 x^{2})}^{3} \cdot (6 x^{2})$ .

Factor $- 27$ out of $- 162$ .

$\sqrt[3]{- 27 (6) x^{8}}$

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

$\sqrt[3]{{(- 3)}^{3} \cdot 6 x^{8}}$

Factor out $x^{6}$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 6 (x^{6} x^{2})}$

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

$\sqrt[3]{{(- 3)}^{3} \cdot 6 ({(x^{2})}^{3} x^{2})}$

Move $6$ .

$\sqrt[3]{{(- 3)}^{3} {(x^{2})}^{3} \cdot 6 x^{2}}$

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

$\sqrt[3]{{(- 3 x^{2})}^{3} \cdot 6 x^{2}}$

Add parentheses.

$\sqrt[3]{{(- 3 x^{2})}^{3} \cdot (6 x^{2})}$

Step 2

Pull terms out from under the radical.

$- 3 x^{2} \sqrt[3]{6 x^{2}}$