1. **State the problem:** Simplify the expression $$(3^2)^{-2}$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \times n} $$ 3. **Apply the rule:** $$ (3^2)^{-2} = 3^{2 \times (-2)} $$ 4. **Multiply the exponents:** $$ 2 \times (-2) = -4 $$ 5. **Rewrite the expression:** $$ 3^{-4} $$ 6. **Interpret negative exponent:** $$ a^{-n} = \frac{1}{a^n} $$ 7. **Rewrite with positive exponent:** $$ 3^{-4} = \frac{1}{3^4} $$ 8. **Calculate $3^4$:** $$ 3^4 = 3 \times 3 \times 3 \times 3 = 81 $$ 9. **Final answer:** $$ \boxed{\frac{1}{81}} $$