Evaluate (6^-4*8^-7)^-9

${(6^{- 4} \cdot 8^{- 7})}^{- 9}$

Step 1

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

${(\frac{1}{6^{4}} \cdot 8^{- 7})}^{- 9}$

Step 2

Raise $6$ to the power of $4$ .

${(\frac{1}{1296} \cdot 8^{- 7})}^{- 9}$

Step 3

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

${(\frac{1}{1296} \cdot \frac{1}{8^{7}})}^{- 9}$

Step 4

Combine.

${(\frac{1 \cdot 1}{1296 \cdot 8^{7}})}^{- 9}$

Step 5

Simplify the expression.

Multiply $1$ by $1$ .

${(\frac{1}{1296 \cdot 8^{7}})}^{- 9}$

Raise $8$ to the power of $7$ .

${(\frac{1}{1296 \cdot 2097152})}^{- 9}$

Multiply $1296$ by $2097152$ .

${(\frac{1}{2717908992})}^{- 9}$

Step 6

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

$2717908992^{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2717908992^{9}$

Decimal Form:

$8.09308672 \cdot 10^{84}$