Question
Is -5^2 equal to (-5^2)?
Answers
GPT-4o
No, \(-5^2\) is not equal to \((-5)^2\). Let's break down the expressions to understand why:
1. \(-5^2\):
- According to the order of operations (PEMDAS/BODMAS), exponentiation is performed before multiplication or negation.
- So, this expression is interpreted as \(-(5^2)\).
- \(5^2\) is 25.
- Therefore, \(-5^2\) equals \(-25\).
2. \((-5)^2\):
- In this case, the parentheses indicate that the negative sign is part of the base being squared.
- So, you are squaring \(-5\).
- \((-5)^2\) equals \((-5) \times (-5)\), which is \(25\).
So, \(-5^2 = -25\), while \((-5)^2 = 25\). Therefore, the two expressions are not equal.
1. \(-5^2\):
- According to the order of operations (PEMDAS/BODMAS), exponentiation is performed before multiplication or negation.
- So, this expression is interpreted as \(-(5^2)\).
- \(5^2\) is 25.
- Therefore, \(-5^2\) equals \(-25\).
2. \((-5)^2\):
- In this case, the parentheses indicate that the negative sign is part of the base being squared.
- So, you are squaring \(-5\).
- \((-5)^2\) equals \((-5) \times (-5)\), which is \(25\).
So, \(-5^2 = -25\), while \((-5)^2 = 25\). Therefore, the two expressions are not equal.