Algebra Examples

$\frac{m^{\frac{2}{3}} n}{m^{2} n^{\frac{1}{2}}}$

Step 1

Move $m^{\frac{2}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

Step 2

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

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Step 2.1

Move $m^{- \frac{2}{3}}$ .

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

Step 2.2

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

$\frac{n}{m^{- \frac{2}{3} + 2} n^{\frac{1}{2}}}$

Step 2.3

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

$\frac{n}{m^{- \frac{2}{3} + 2 \cdot \frac{3}{3}} n^{\frac{1}{2}}}$

Step 2.4

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

$\frac{n}{m^{- \frac{2}{3} + \frac{2 \cdot 3}{3}} n^{\frac{1}{2}}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{n}{m^{\frac{- 2 + 2 \cdot 3}{3}} n^{\frac{1}{2}}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $2$ by $3$ .

$\frac{n}{m^{\frac{- 2 + 6}{3}} n^{\frac{1}{2}}}$

Step 2.6.2

Add $- 2$ and $6$ .

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

Step 3

Move $n^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 4

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

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Step 4.1

Multiply $n$ by $n^{- \frac{1}{2}}$ .

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Step 4.1.1

Raise $n$ to the power of $1$ .

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

Step 4.1.2

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

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

Step 4.2

Write $1$ as a fraction with a common denominator.

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

Step 4.3

Combine the numerators over the common denominator.

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

Step 4.4

Subtract $1$ from $2$ .

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