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

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

Step 1

Raise $9$ to the power of $6$ .

${(531441 \cdot 7^{- 9})}^{- 4}$

Step 2

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

${(531441 \cdot \frac{1}{7^{9}})}^{- 4}$

Step 3

Raise $7$ to the power of $9$ .

${(531441 \cdot \frac{1}{40353607})}^{- 4}$

Step 4

Combine $531441$ and $\frac{1}{40353607}$ .

${(\frac{531441}{40353607})}^{- 4}$

Step 5

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

${(\frac{40353607}{531441})}^{4}$

Step 6

Apply the product rule to $\frac{40353607}{531441}$ .

$\frac{40353607^{4}}{531441^{4}}$

Step 7

Raise $531441$ to the power of $4$ .

$\frac{40353607^{4}}{79766443076872500000000}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{40353607^{4}}{79766443076872500000000}$

Decimal Form:

$33243689.2454152$