Algebra Examples

${(\frac{a^{- 7}}{a^{- 8}})}^{- 6}$

Step 1

Move $a^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(a^{- 7} a^{8})}^{- 6}$

Step 2

Multiply $a^{- 7}$ by $a^{8}$ by adding the exponents.

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Step 2.1

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

${(a^{- 7 + 8})}^{- 6}$

Step 2.2

Add $- 7$ and $8$ .

${(a^{1})}^{- 6}$

Step 3

Simplify $a^{1}$ .

$a^{- 6}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a^{6}}$