Precalculus Examples

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

Step 1

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

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

Step 2

Multiply $m^{4}$ by $m^{2}$ by adding the exponents.

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Step 2.1

Move $m^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $4$ .

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

Step 3

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

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

Step 4

Multiply $n^{3}$ by $n$ by adding the exponents.

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Step 4.1

Multiply $n^{3}$ by $n$ .

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Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.2

Add $3$ and $1$ .

${(\frac{n^{4}}{m^{6}})}^{2}$

Step 5

Apply the product rule to $\frac{n^{4}}{m^{6}}$ .

$\frac{{(n^{4})}^{2}}{{(m^{6})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{n^{4 \cdot 2}}{{(m^{6})}^{2}}$

Step 6.2

Multiply $4$ by $2$ .

$\frac{n^{8}}{{(m^{6})}^{2}}$

Step 7

Multiply the exponents in ${(m^{6})}^{2}$ .

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Step 7.1

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

$\frac{n^{8}}{m^{6 \cdot 2}}$

Step 7.2

Multiply $6$ by $2$ .

$\frac{n^{8}}{m^{12}}$