1. **State the problem:** Simplify the expression $$\frac{3^6}{3^2}$$. 2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule:** $$\frac{3^6}{3^2} = 3^{6-2} = 3^4$$. 4. **Calculate the power:** $$3^4 = 3 \times 3 \times 3 \times 3 = 81$$. 5. **Final answer:** $$\boxed{81}$$