The problem asks you to evaluate two expressions:

1. $(-4)^2$
2. $(-4)^3$

Let's break this down:

1. $(-4)^2$:

   • Squaring $-4$ means multiplying $-4$ by itself.
   • $(-4) \times (-4) = 16$ (since multiplying two negative numbers results in a positive number).

2. $(-4)^3$:

   • Cubing $-4$ means multiplying $-4$ by itself three times.
   • $(-4) \times (-4) \times (-4) = -64$ (multiplying two negative numbers gives a positive, and then multiplying by a negative number results in a negative number).

Final Answers:

• $(-4)^2 = 16$
• $(-4)^3 = -64$

If you want to, enter these values in the corresponding boxes.

Would you like more details on exponentiation or any other related topic?

Here are some related questions to consider:

1. What is the difference between even and odd exponents for negative bases?
2. How would the result change if the base was a positive number instead?
3. Can you explain the significance of parentheses in expressions like $(-4)^2$ versus $-4^2$?
4. What are some real-life applications of using exponents?
5. How would you compute higher powers, such as $(-4)^5$?

Tip:

Always be careful with parentheses when dealing with negative numbers and exponents; they can significantly change the outcome.