Simplify cube root of 192x^8

$\sqrt[3]{192 x^{8}}$

Step 1

Rewrite $192 x^{8}$ as ${(4 x^{2})}^{3} \cdot (3 x^{2})$ .

Factor $64$ out of $192$ .

$\sqrt[3]{64 (3) x^{8}}$

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

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

Factor out $x^{6}$ .

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

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

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

Move $3$ .

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

Rewrite $4^{3} {(x^{2})}^{3}$ as ${(4 x^{2})}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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