Simplify cube root of 24x^6

$\sqrt[3]{24 x^{6}}$

Step 1

Rewrite $24 x^{6}$ as ${(2 x^{2})}^{3} \cdot 3$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) x^{6}}$

Rewrite $8$ as $2^{3}$ .

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

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

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

Move $3$ .

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

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

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

Step 2

Pull terms out from under the radical.

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