Algebra Examples

$\sqrt[5]{m^{5} n^{- 5}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt[5]{m^{5} \frac{1}{n^{5}}}$

Step 2

Combine $m^{5}$ and $\frac{1}{n^{5}}$ .

$\sqrt[5]{\frac{m^{5}}{n^{5}}}$

Step 3

Rewrite $\frac{m^{5}}{n^{5}}$ as ${(\frac{m}{n})}^{5}$ .

$\sqrt[5]{{(\frac{m}{n})}^{5}}$

Step 4

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

$\frac{m}{n}$