Simplify cube root of 108x^6

$\sqrt[3]{108 x^{6}}$

Step 1

Rewrite $108 x^{6}$ as ${(3 x^{2})}^{3} \cdot 4$ .

Factor $27$ out of $108$ .

$\sqrt[3]{27 (4) x^{6}}$

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} \cdot 4 x^{6}}$

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

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

Move $4$ .

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

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

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

Step 2

Pull terms out from under the radical.

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