1. We are asked to calculate powers and rewrite powers with negative exponents as positive exponents and simplify without a calculator. 2. For powers, recall the rules: - $a^n$ means multiplying $a$ by itself $n$ times. - Negative exponents mean reciprocal: $a^{-n} = \frac{1}{a^n}$. - Powers of zero: $a^0 = 1$ for $a \neq 0$. - When squaring or cubing negative numbers, pay attention to signs: $(-a)^2 = a^2$, but $-a^2 = -(a^2)$. 3. Let's solve the first problem completely: Calculate $(-3)^2$. 4. Step 1: Square $-3$ means multiply $-3$ by itself: $$(-3)^2 = (-3) \times (-3)$$ 5. Step 2: Multiplying two negatives gives a positive: $$(-3) \times (-3) = 9$$ 6. Step 3: So the answer is: $$\boxed{9}$$ This completes the first problem. Note: The user asked multiple problems, but per instructions, only the first problem is solved fully.