Precalculus Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

Multiply $n^{3}$ by $n^{2}$ by adding the exponents.

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Step 2.1.1

Move $n^{2}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add $2$ and $3$ .

${(\frac{3 m^{4}}{2 m^{0} n^{5}})}^{- 2}$

Step 2.2

Simplify $2 m^{0} n^{5}$ .

${(\frac{3 m^{4}}{2 n^{5}})}^{- 2}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{2 n^{5}}{3 m^{4}})}^{2}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{2 n^{5}}{3 m^{4}}$ .

$\frac{{(2 n^{5})}^{2}}{{(3 m^{4})}^{2}}$

Step 4.2

Apply the product rule to $2 n^{5}$ .

$\frac{2^{2} {(n^{5})}^{2}}{{(3 m^{4})}^{2}}$

Step 4.3

Apply the product rule to $3 m^{4}$ .

$\frac{2^{2} {(n^{5})}^{2}}{3^{2} {(m^{4})}^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $2$ to the power of $2$ .

$\frac{4 {(n^{5})}^{2}}{3^{2} {(m^{4})}^{2}}$

Step 5.2

Multiply the exponents in ${(n^{5})}^{2}$ .

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Step 5.2.1

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

$\frac{4 n^{5 \cdot 2}}{3^{2} {(m^{4})}^{2}}$

Step 5.2.2

Multiply $5$ by $2$ .

$\frac{4 n^{10}}{3^{2} {(m^{4})}^{2}}$

Step 6

Simplify the denominator.

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Step 6.1

Raise $3$ to the power of $2$ .

$\frac{4 n^{10}}{9 {(m^{4})}^{2}}$

Step 6.2

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

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Step 6.2.1

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

$\frac{4 n^{10}}{9 m^{4 \cdot 2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{4 n^{10}}{9 m^{8}}$