https://file.aiquickdraw.com/mathbot/file/1727319053999i82msj6h.jpg

In the image, the exercise discusses the proper interpretation of expressions involving negative numbers and exponents, specifically focusing on how the order of operations affects the outcome.

### Part (a): Fill in:
The expression is \(-5^2\). It's important to understand that according to the order of operations, exponents are evaluated before applying the negative sign unless parentheses are used.

- The expression \(-5^2\) is interpreted as \(-(5^2)\), meaning the negative sign applies *after* squaring the 5.
- Therefore:
  \[
  -5^2 = -(5^2) = -(25) = -25
  \]

### Part (b): Evaluate the expression
In part (b), you are asked to evaluate the same expression, confirming that exponents take precedence over the negative sign:

- From part (a), we know:
  \[
  -5^2 = -25
  \]

Let me know if you'd like any further clarification or details!

### Related questions:
1. What happens if you write \((-5)^2\) instead of \(-5^2\)?
2. How does the order of operations (PEMDAS) affect other types of expressions?
3. What is the difference between \(-x^2\) and \((-x)^2\)?
4. Can you evaluate \(-6^2\) and explain how it differs from \((-6)^2\)?
5. Why do exponents come before multiplication or negation in mathematical expressions?

### Tip:
Always apply exponents before negating values, unless the negative sign is enclosed within parentheses!

Fill in and evaluate the expression for the exercise: -5^2.

Explore how to correctly interpret and evaluate expressions with negative bases and exponents, such as -5^2. This guide emphasizes the importance of the order of operations in simplifying expressions and helps clarify common misconceptions. Suitable for Middle School and High School students.

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