Simplify cube root of 192x^4

$\sqrt[3]{192 x^{4}}$

Step 1

Rewrite $192 x^{4}$ as ${(4 x)}^{3} \cdot (3 x)$ .

Factor $64$ out of $192$ .

$\sqrt[3]{64 (3) x^{4}}$

Rewrite $64$ as $4^{3}$ .

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

Factor out $x^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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