Simplify fourth root of 16x^6

$\sqrt[4]{16 x^{6}}$

Step 1

Rewrite $16 x^{6}$ as ${(2 x)}^{4} x^{2}$ .

Rewrite $16$ as $2^{4}$ .

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

Factor out $x^{4}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$2 x \sqrt{\sqrt{x^{2}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$2 x \sqrt{x}$