Basic Math Examples

${(8^{- 2} \cdot 9^{- 3})}^{- 3}$

Step 1

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

${(\frac{1}{8^{2}} \cdot 9^{- 3})}^{- 3}$

Step 2

Raise $8$ to the power of $2$ .

${(\frac{1}{64} \cdot 9^{- 3})}^{- 3}$

Step 3

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

${(\frac{1}{64} \cdot \frac{1}{9^{3}})}^{- 3}$

Step 4

Combine.

${(\frac{1 \cdot 1}{64 \cdot 9^{3}})}^{- 3}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $1$ by $1$ .

${(\frac{1}{64 \cdot 9^{3}})}^{- 3}$

Step 5.2

Raise $9$ to the power of $3$ .

${(\frac{1}{64 \cdot 729})}^{- 3}$

Step 5.3

Multiply $64$ by $729$ .

${(\frac{1}{46656})}^{- 3}$

Step 6

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

$46656^{3}$

Step 7

Raise $46656$ to the power of $3$ .

$101559956668416$