Simplify (6^-3)/((6^-6)^2)

$\frac{6^{- 3}}{{(6^{- 6})}^{2}}$

Step 1

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

$\frac{1}{{(6^{- 6})}^{2} \cdot 6^{3}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(6^{- 6})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{6^{- 6 \cdot 2} \cdot 6^{3}}$

Multiply $- 6$ by $2$ .

$\frac{1}{6^{- 12} \cdot 6^{3}}$

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

$\frac{1}{\frac{1}{6^{12}} \cdot 6^{3}}$

Raise $6$ to the power of $12$ .

$\frac{1}{\frac{1}{2176782336} \cdot 6^{3}}$

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

$\frac{1}{\frac{1}{2176782336} \cdot 216}$

Step 3

Simplify terms.

Combine $\frac{1}{2176782336}$ and $216$ .

$\frac{1}{\frac{216}{2176782336}}$

Cancel the common factor of $216$ and $2176782336$ .

Factor $216$ out of $216$ .

$\frac{1}{\frac{216 (1)}{2176782336}}$

Cancel the common factors.

Factor $216$ out of $2176782336$ .

$\frac{1}{\frac{216 \cdot 1}{216 \cdot 10077696}}$

Cancel the common factor.

$\frac{1}{\frac{216 \cdot 1}{216 \cdot 10077696}}$

Rewrite the expression.

$\frac{1}{\frac{1}{10077696}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 10077696$

Step 5

Multiply $10077696$ by $1$ .

$10077696$