Simplify cube root of 54x^6

$\sqrt[3]{54 x^{6}}$

Step 1

Rewrite $54 x^{6}$ as ${(3 x^{2})}^{3} \cdot 2$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{6}}$

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

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

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

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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