Algebra Examples

$\sqrt[4]{\frac{m^{10}}{16}}$

Step 1

Rewrite $\frac{m^{10}}{16}$ as ${(\frac{m^{2}}{2})}^{4} m^{2}$ .

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Step 1.1

Factor the perfect power ${(m^{2})}^{4}$ out of $m^{10}$ .

$\sqrt[4]{\frac{{(m^{2})}^{4} m^{2}}{16}}$

Step 1.2

Factor the perfect power $2^{4}$ out of $16$ .

$\sqrt[4]{\frac{{(m^{2})}^{4} m^{2}}{2^{4} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(m^{2})}^{4} m^{2}}{2^{4} \cdot 1}$ .

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

Step 2

Pull terms out from under the radical.

$\frac{m^{2}}{2} \sqrt[4]{m^{2}}$

Step 3

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

$\frac{m^{2}}{2} \sqrt{\sqrt{m^{2}}}$

Step 4

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

$\frac{m^{2}}{2} \sqrt{m}$

Step 5

Combine $\frac{m^{2}}{2}$ and $\sqrt{m}$ .

$\frac{m^{2} \sqrt{m}}{2}$