To solve $6^{-2}$, we apply the negative exponent rule, which states that $a^{-n} = \frac{1}{a^n}$.

1. Rewrite the expression: $6^{-2} = \frac{1}{6^2}$

2. Calculate $6^2$: $6^2 = 36$

3. Substitute this back into the expression: $6^{-2} = \frac{1}{36}$

The final answer is: $\boxed{\frac{1}{36}}$

Would you like a further explanation or details on exponents? Here are some related questions to explore:

1. What is the general rule for simplifying negative exponents?
2. How does the negative exponent rule apply to fractions?
3. How do you solve $(6^{-2})^3$?
4. What are some practical applications of negative exponents in real-world scenarios?
5. How can negative exponents be used in simplifying algebraic expressions?

Tip: When dealing with negative exponents, always start by rewriting them as reciprocals for better clarity.