Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Anything raised to $1$ is the base itself.

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

Step 6

Anything raised to $1$ is the base itself.

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