Let's break this down carefully:

1. \(-4^2\) means \(-(4^2)\). So, \(-4^2 = -(16) = -16\).
2. \((-4)^2\) means squaring \(-4\), which gives \((-4) \times (-4) = 16\).

Now combine the two:

\[
-4^2 + (-4)^2 = -16 + 16 = 0
\]

So, the final result is \(0\).

Would you like more details on why \(-4^2\) is negative while \((-4)^2\) is positive? Here are a few related questions to think about:

1. How does the placement of parentheses affect the result of squaring negative numbers?
2. What is the difference between \(-x^2\) and \((-x)^2\)?
3. What is the square of \(-5\) compared to \((-5)^2\)?
4. How would the result change if we had a cube instead of a square, such as \(-4^3\) and \((-4)^3\)?
5. What is the general rule for the sign of powers when working with negative numbers?

**Tip:** Parentheses are essential when working with negative numbers and exponents—use them carefully!

Learn how to evaluate expressions like -4^2 and (-4)^2, understand the impact of parentheses on exponentiation, and why -4^2 equals -16 while (-4)^2 equals 16. Suitable for students in Grades 6-8, this problem explores exponents, negative numbers, and the order of operations.

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