Simplify cube root of 108x^4

$\sqrt[3]{108 x^{4}}$

Step 1

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

Factor $27$ out of $108$ .

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

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

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

Factor out $x^{3}$ .

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

Move $4$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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