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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.

Evaluate the expressions (-4)^2 and (-4)^3.

Learn how to evaluate exponents involving negative numbers with detailed examples. This problem covers key mathematical concepts such as exponentiation and the properties of negative numbers. Suitable for students in Grades 6-8.

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