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

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

Step 1

Move $5^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $5^{6}$ by $5^{3}$ by adding the exponents.

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

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

Add $6$ and $3$ .

${(\frac{1}{5^{9}})}^{- 6}$

Step 3

Raise $5$ to the power of $9$ .

${(\frac{1}{1953125})}^{- 6}$

Step 4

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

$1953125^{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$1953125^{6}$

Decimal Form:

$5.55111512 \cdot 10^{37}$