Algebra Examples

$\sqrt[10]{\sqrt[5]{x^{20}}}$

Step 1

Rewrite $x^{20}$ as ${(x^{4})}^{5}$ .

$\sqrt[10]{\sqrt[5]{{(x^{4})}^{5}}}$

Step 2

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

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

Step 3

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

$\sqrt[10]{{(x^{2})}^{2}}$

Step 4

Rewrite $\sqrt[10]{{(x^{2})}^{2}}$ as $\sqrt[5]{\sqrt{{(x^{2})}^{2}}}$ .

$\sqrt[5]{\sqrt{{(x^{2})}^{2}}}$

Step 5

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

$\sqrt[5]{x^{2}}$