Simplify fourth root of x^10

$\sqrt[4]{x^{10}}$

Step 1

Rewrite $x^{10}$ as ${(x^{2})}^{4} x^{2}$ .

Factor out $x^{8}$ .

$\sqrt[4]{x^{8} x^{2}}$

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

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

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