Question

Explain the difference between (-10) to the power of 2 and -10 to the power of 2 What are the values of each expression?

Answer 1

The difference between \((-10)^2\) and \(-10^2\) lies in how the negative sign is treated in each expression.

1. **\((-10)^2\)**:
- Here, the parentheses indicate that the negative sign is included in the base. Therefore, you are squaring \(-10\).
- Calculation:
\[
(-10) \times (-10) = 100
\]
- Value: \((-10)^2 = 100\)

2. **\(-10^2\)**:
- In this case, the absence of parentheses indicates that only \(10\) is being squared first, and then the negative sign is applied to the result.
- Calculation:
\[
- (10 \times 10) = -100
\]
- Value: \(-10^2 = -100\)

In summary:
- \((-10)^2 = 100\)
- \(-10^2 = -100\)