Simplify ((3^-6)/(3^0))^-3

${(\frac{3^{- 6}}{3^{0}})}^{- 3}$

Step 1

Move $3^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{3^{0} \cdot 3^{6}})}^{- 3}$

Step 2

Multiply $3^{0}$ by $3^{6}$ by adding the exponents.

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

${(\frac{1}{3^{0 + 6}})}^{- 3}$

Add $0$ and $6$ .

${(\frac{1}{3^{6}})}^{- 3}$

Step 3

Raise $3$ to the power of $6$ .

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

Step 4

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

$729^{3}$

Step 5

Raise $729$ to the power of $3$ .

$387420489$