1. **State the problem:** Evaluate the expressions $(-4)^2$ and $(-2)^3$. 2. **Recall the rules for exponents:** - When raising a number to an exponent, multiply the base by itself as many times as the exponent indicates. - For negative bases, parentheses matter: $(-a)^n$ means the negative sign is included in the base. - If $n$ is even, $(-a)^n$ is positive because multiplying an even number of negatives results in a positive. - If $n$ is odd, $(-a)^n$ is negative because multiplying an odd number of negatives results in a negative. 3. **Evaluate $(-4)^2$:** $$(-4)^2 = (-4) \times (-4) = 16$$ Since the exponent 2 is even, the result is positive. 4. **Evaluate $(-2)^3$:** $$(-2)^3 = (-2) \times (-2) \times (-2) = 4 \times (-2) = -8$$ Since the exponent 3 is odd, the result is negative. **Final answers:** $$(-4)^2 = 16$$ $$(-2)^3 = -8$$