Simplify cube root of -108x^8

$\sqrt[3]{- 108 x^{8}}$

Step 1

Rewrite $- 108 x^{8}$ as ${(- 3 x^{2})}^{3} \cdot (4 x^{2})$ .

Factor $- 27$ out of $- 108$ .

$\sqrt[3]{- 27 (4) x^{8}}$

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

$\sqrt[3]{{(- 3)}^{3} \cdot 4 x^{8}}$

Factor out $x^{6}$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 4 (x^{6} x^{2})}$

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

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

Move $4$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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