The expression \(-2^2\) can be interpreted in different ways depending on the order of operations. In mathematical expressions, exponents are evaluated before negations unless parentheses dictate otherwise.

### Order of Operations (PEMDAS/BODMAS)

- **P/B:** Parentheses/Brackets
- **E/O:** Exponents/Orders (such as powers and roots)
- **MD:** Multiplication and Division (from left to right)
- **AS:** Addition and Subtraction (from left to right)

### Interpretation of \(-2^2\)

1. **Without Parentheses:**

   The expression is \(-2^2\), which means the negative sign is applied after the exponentiation:

   \[
   -2^2 = -(2^2) = -(4) = -4
   \]

2. **With Parentheses:**

   If the expression were written as \((-2)^2\), the negative sign is part of the base that is being squared:

   \[
   (-2)^2 = (-2) \times (-2) = 4
   \]

Thus, the expression \(-2^2\) is \(-4\) when evaluated without parentheses, as the exponent takes precedence over the negation.

If you have further questions or need clarification, let me know!

Here are some related questions to explore further:

1. How do parentheses affect the order of operations?
2. What is the difference between \(-2^2\) and \((-2)^2\)?
3. Can exponents be negative, and how are they evaluated?
4. How do you evaluate expressions with multiple exponents?
5. What is the meaning of a fractional exponent?
6. How do you simplify expressions with mixed operations?
7. What are the common mistakes in evaluating exponents?
8. How do you apply exponents to algebraic expressions?

**Tip:** Always use parentheses to clarify which part of the expression is to be raised to a power, especially when dealing with negative numbers.

Explore the expression -2^2 and understand how order of operations affects its evaluation. Learn about exponents, negative numbers, and the importance of parentheses in mathematical expressions. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation