To simplify the given expression $(6^{-2})^{-1}$, we can use the property of exponents that states:

$(a^m)^n = a^{m \cdot n}$

Steps:

1. The expression is $(6^{-2})^{-1}$.
2. Using the exponent rule mentioned above, multiply the exponents: $6^{-2 \cdot (-1)} = 6^{2}$
3. Therefore, $(6^{-2})^{-1} = 6^2$.

Final Answer:

$6^2 = 36$

So, the expression is equivalent to 36.

Would you like further details or explanations?

Related Questions:

1. How do you simplify expressions with negative exponents?
2. What are the rules of exponents for multiplication and division?
3. How do fractional exponents work?
4. How do negative powers of a number affect the result?
5. Can you show examples of simplifying complex exponent expressions?

Tip: Always check for exponent rules like $(a^m)^n = a^{m \cdot n}$, which help simplify expressions efficiently.