Simplify fourth root of 162x^6

$\sqrt[4]{162 x^{6}}$

Rewrite $162 x^{6}$ as ${(3 x)}^{4} \cdot (2 x^{2})$ .

Factor $81$ out of $162$ .

$\sqrt[4]{81 (2) x^{6}}$

Rewrite $81$ as $3^{4}$ .

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

Factor out $x^{4}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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