Evaluate ((3^-1)/(3^6))^-5

${(\frac{3^{- 1}}{3^{6}})}^{- 5}$

Step 1

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

${(\frac{1}{3^{6} \cdot 3})}^{- 5}$

Step 2

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

Multiply $3^{6}$ by $3$ .

Raise $3$ to the power of $1$ .

${(\frac{1}{3^{6} \cdot 3^{1}})}^{- 5}$

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

${(\frac{1}{3^{6 + 1}})}^{- 5}$

Add $6$ and $1$ .

${(\frac{1}{3^{7}})}^{- 5}$

Step 3

Raise $3$ to the power of $7$ .

${(\frac{1}{2187})}^{- 5}$

Step 4

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

$2187^{5}$

Step 5

Raise $2187$ to the power of $5$ .

$50031545098999700$

Step 6

The result can be shown in multiple forms.

Exact Form:

$50031545098999700$

Decimal Form:

$5.0031545 \cdot 10^{16}$