1. The problem involves evaluating two expressions: $(-3)^4$ and $(-2)^3$. 2. First, calculate $(-3)^4$. This means multiplying $-3$ by itself 4 times: $$(-3)^4 = (-3) \times (-3) \times (-3) \times (-3)$$ 3. Calculate step-by-step: $$(-3) \times (-3) = 9$$ $$9 \times (-3) = -27$$ $$-27 \times (-3) = 81$$ 4. Hence, $(-3)^4 = 81$ (this matches the given result). 5. Next, calculate $(-2)^3$ which means multiplying $-2$ by itself 3 times: $$(-2)^3 = (-2) \times (-2) \times (-2)$$ 6. Calculate step-by-step: $$(-2) \times (-2) = 4$$ $$4 \times (-2) = -8$$ 7. So, $(-2)^3 = -8$. Final answers: $$(-3)^4 = 81$$ $$(-2)^3 = -8$$