Math Problem Statement

-5 the power of 2

Solution

The expression "-5 to the power of 2" can be interpreted in two ways depending on how it's written:

  1. (5)2(-5)^2: This means the base is 5-5, and you're squaring it. So, you multiply 5-5 by 5-5: (5)2=(5)×(5)=25(-5)^2 = (-5) \times (-5) = 25

  2. 52-5^2: This means the negative sign is outside the exponentiation. So, you're squaring 5 and then applying the negative sign: 52=(5×5)=25-5^2 = -(5 \times 5) = -25

Let me know if you would like any clarifications or details on this!

Here are five related questions:

  1. What is the square of any negative number?
  2. How do parentheses affect exponentiation?
  3. What is the cube of 5-5?
  4. How does order of operations apply to powers and negatives?
  5. What is the power of zero, (a0)(a^0), for any number aa?

Tip: Parentheses play a crucial role in math, especially in expressions with exponents and negative numbers. Always watch for them!

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Negative Numbers
Order of Operations

Formulas

(-a)^n = (-a) * (-a) * ... (n times)
-a^n = -(a * a * ... n times)

Theorems

Laws of Exponents
Order of Operations (PEMDAS)

Suitable Grade Level

Grades 6-8