Simplify fourth root of x^14

$\sqrt[4]{x^{14}}$

Step 1

Rewrite $x^{14}$ as ${(x^{3})}^{4} x^{2}$ .

Factor out $x^{12}$ .

$\sqrt[4]{x^{12} x^{2}}$

Rewrite $x^{12}$ as ${(x^{3})}^{4}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

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

$x^{3} \sqrt{x}$