Evaluate (a^-7*b^-2)^-9

${(a^{- 7} \cdot b^{- 2})}^{- 9}$

Step 1

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

${(\frac{1}{a^{7}} \cdot b^{- 2})}^{- 9}$

Step 2

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

${(\frac{1}{a^{7}} \cdot \frac{1}{b^{2}})}^{- 9}$

Step 3

Combine.

${(\frac{1 \cdot 1}{a^{7} b^{2}})}^{- 9}$

Step 4

Multiply $1$ by $1$ .

${(\frac{1}{a^{7} b^{2}})}^{- 9}$

Step 5

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

${(a^{7} b^{2})}^{9}$

Step 6

Apply the product rule to $a^{7} b^{2}$ .

${(a^{7})}^{9} {(b^{2})}^{9}$

Step 7

Multiply the exponents in ${(a^{7})}^{9}$ .

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

$a^{7 \cdot 9} {(b^{2})}^{9}$

Multiply $7$ by $9$ .

$a^{63} {(b^{2})}^{9}$

Step 8

Multiply the exponents in ${(b^{2})}^{9}$ .

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

$a^{63} b^{2 \cdot 9}$

Multiply $2$ by $9$ .

$a^{63} b^{18}$