Basic Math Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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Step 2.1

Move $m$ .

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

Step 2.2

Multiply $m$ by $m^{\frac{1}{2}}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $2$ and $1$ .

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

Step 3

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

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Step 3.1

Move $n^{2}$ .

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

Step 3.2

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

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

Step 3.3

Subtract $2$ from $2$ .

${(\frac{m^{\frac{3}{2}} n^{0}}{n^{- 2}})}^{\frac{1}{4}}$

Step 4

Simplify $m^{\frac{3}{2}} n^{0}$ .

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

Step 5

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

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

Step 6

Apply the product rule to $m^{\frac{3}{2}} n^{2}$ .

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

Step 7

Multiply the exponents in ${(m^{\frac{3}{2}})}^{\frac{1}{4}}$ .

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Step 7.1

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

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

Step 7.2

Multiply $\frac{3}{2} \cdot \frac{1}{4}$ .

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Step 7.2.1

Multiply $\frac{3}{2}$ by $\frac{1}{4}$ .

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

Step 7.2.2

Multiply $2$ by $4$ .

$m^{\frac{3}{8}} {(n^{2})}^{\frac{1}{4}}$

Step 8

Multiply the exponents in ${(n^{2})}^{\frac{1}{4}}$ .

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Step 8.1

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

$m^{\frac{3}{8}} n^{2 (\frac{1}{4})}$

Step 8.2

Cancel the common factor of $2$ .

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Step 8.2.1

Factor $2$ out of $4$ .

$m^{\frac{3}{8}} n^{2 \frac{1}{2 (2)}}$

Step 8.2.2

Cancel the common factor.

$m^{\frac{3}{8}} n^{2 \frac{1}{2 \cdot 2}}$

Step 8.2.3

Rewrite the expression.

$m^{\frac{3}{8}} n^{\frac{1}{2}}$