Algebra Examples

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

Step 1

Move $m^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

Multiply $m^{2}$ by $m^{- \frac{1}{3}}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.3

Combine $2$ and $\frac{3}{3}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $3$ .

${(m^{\frac{6 - 1}{3}})}^{- \frac{1}{2}}$

Step 2.5.2

Subtract $1$ from $6$ .

${(m^{\frac{5}{3}})}^{- \frac{1}{2}}$

Step 3

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

${\sqrt[3]{m^{5}}}^{- \frac{1}{2}}$

Step 4

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

$\frac{1}{{\sqrt[3]{m^{5}}}^{\frac{1}{2}}}$

Step 5

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

$\frac{1}{\sqrt{{\sqrt[3]{m^{5}}}^{1}}}$

Step 6

Anything raised to $1$ is the base itself.

$\frac{1}{\sqrt{\sqrt[3]{m^{5}}}}$