Let's solve the expression step by step:

Given expression:
\[
-4^2 + 8(4) + 16
\]

1. **Evaluate \(-4^2\):**

   It's important to note that \(-4^2\) means \(-(4^2)\), not \((-4)^2\). So:
   \[
   -4^2 = -(4 \times 4) = -16
   \]
   
   Now the expression is:
   \[
   -16 + 8(4) + 16
   \]

2. **Evaluate \(8(4)\):**
   \[
   8 \times 4 = 32
   \]
   
   Now the expression becomes:
   \[
   -16 + 32 + 16
   \]

3. **Add the numbers together:**
   \[
   -16 + 32 = 16
   \]
   \[
   16 + 16 = 32
   \]

So, the final result is:
\[
32
\]

Do you want more details on any of these steps or have any questions?

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Here are five related questions you might find interesting:
1. How does the interpretation of the negative sign before an exponent affect the result?
2. What is the difference between \(-4^2\) and \((-4)^2\)?
3. How would the expression change if we used \((-4)^2\) instead of \(-4^2\)?
4. What happens to the expression if you change the multiplication to addition inside the parentheses?
5. How can this approach be applied to more complex expressions with multiple operations?

**Tip:** Always remember that exponents are applied before multiplication or negation when following the order of operations.

Learn how to solve the expression -4^2 + 8(4) + 16 step-by-step. Understand the order of operations and the evaluation of negative exponents and multiplication. Suitable for Grades 6-8.

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