1. **State the problem:** Simplify and evaluate the expression $$(-3)^4 + \frac{(-3)^6}{(-3)^5} - (-3)^2$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Evaluate powers carefully, noting that $$(-3)^n$$ means the entire base $-3$ is raised to the power $n$. 3. **Evaluate each term:** - $$(-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81$$ because an even power of a negative number is positive. - $$\frac{(-3)^6}{(-3)^5} = (-3)^{6-5} = (-3)^1 = -3$$. - $$(-3)^2 = 9$$. 4. **Substitute back:** $$81 + (-3) - 9$$ 5. **Simplify:** $$81 - 3 - 9 = 78 - 9 = 69$$. **Final answer:** $$69$$.