Algebra Examples

$\frac{m^{\frac{3}{4}} n^{- \frac{1}{4}}}{{(m^{2} n)}^{\frac{1}{2}}}$

Step 1

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{\sqrt[4]{m^{3}} n^{- \frac{1}{4}}}{{(m^{2} n)}^{\frac{1}{2}}}$

Step 2

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

$\frac{\sqrt[4]{m^{3}} \frac{1}{n^{\frac{1}{4}}}}{{(m^{2} n)}^{\frac{1}{2}}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{\sqrt[4]{m^{3}} \frac{1}{\sqrt[4]{n^{1}}}}{{(m^{2} n)}^{\frac{1}{2}}}$

Step 4

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{\sqrt[4]{m^{3}} \frac{1}{\sqrt[4]{n^{1}}}}{\sqrt{{(m^{2} n)}^{1}}}$

Step 5

Anything raised to $1$ is the base itself.

$\frac{\sqrt[4]{m^{3}} \frac{1}{\sqrt[4]{n}}}{\sqrt{{(m^{2} n)}^{1}}}$

Step 6

Anything raised to $1$ is the base itself.

$\frac{\sqrt[4]{m^{3}} \frac{1}{\sqrt[4]{n}}}{\sqrt{m^{2} n}}$