Algebra Examples

${(\frac{- 3^{2} b^{- 2}}{a^{8} c^{- 4}})}^{- 1}$

Step 1

Simplify.

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Step 1.1

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

${(\frac{- 3^{2}}{a^{8} c^{- 4} b^{2}})}^{- 1}$

Step 1.2

Move $c^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{- 3^{2} c^{4}}{a^{8} b^{2}})}^{- 1}$

Step 2

Simplify the numerator.

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Step 2.1

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

${(\frac{- 1 \cdot 9 c^{4}}{a^{8} b^{2}})}^{- 1}$

Step 2.2

Multiply $- 1$ by $9$ .

${(\frac{- 9 c^{4}}{a^{8} b^{2}})}^{- 1}$

Step 3

Move the negative in front of the fraction.

${(- \frac{9 c^{4}}{a^{8} b^{2}})}^{- 1}$

Step 4

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

$- \frac{a^{8} b^{2}}{9 c^{4}}$