Basic Math Examples

$\sqrt[21]{x^{45}}$

Step 1

Rewrite $x^{45}$ as ${(x^{2})}^{21} x^{3}$ .

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Step 1.1

Factor out $x^{42}$ .

$\sqrt[21]{x^{42} x^{3}}$

Step 1.2

Rewrite $x^{42}$ as ${(x^{2})}^{21}$ .

$\sqrt[21]{{(x^{2})}^{21} x^{3}}$

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt[21]{x^{3}}$

Step 3

Rewrite $\sqrt[21]{x^{3}}$ as $\sqrt[7]{\sqrt[3]{x^{3}}}$ .

$x^{2} \sqrt[7]{\sqrt[3]{x^{3}}}$

Step 4

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

$x^{2} \sqrt[7]{x}$