Simplify eighth root of x^20

$\sqrt[8]{x^{20}}$

Step 1

Rewrite $x^{20}$ as ${(x^{2})}^{8} x^{4}$ .

Factor out $x^{16}$ .

$\sqrt[8]{x^{16} x^{4}}$

Rewrite $x^{16}$ as ${(x^{2})}^{8}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $\sqrt[8]{x^{4}}$ as $\sqrt{\sqrt[4]{x^{4}}}$ .

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

Step 4

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

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