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

Multiply the exponents in ${(m^{\frac{5}{3}})}^{- \frac{1}{2}}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 3.2

Multiply $\frac{5}{3} (- \frac{1}{2})$ .

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Step 3.2.1

Multiply $\frac{5}{3}$ by $\frac{1}{2}$ .

$m^{- \frac{5}{3 \cdot 2}}$

Step 3.2.2

Multiply $3$ by $2$ .

$m^{- \frac{5}{6}}$

Step 4

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

$\frac{1}{m^{\frac{5}{6}}}$