Math Problem Statement

Solve 5^2 · 5^-2

Solution

The problem is asking to solve the expression 52525^2 \cdot 5^{-2}.

Step-by-Step Solution:

  1. Apply the Product of Powers Rule: When multiplying two powers with the same base, you add the exponents. 5252=52+(2)=505^2 \cdot 5^{-2} = 5^{2 + (-2)} = 5^0

  2. Evaluate 505^0: Any number raised to the power of zero is equal to 1. 50=15^0 = 1

Thus, the correct answer is 1, not 625.

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

Related Questions:

  1. What is the product of 34343^4 \cdot 3^{-4}?
  2. How do you solve 23252^3 \cdot 2^{-5}?
  3. What is the value of 707^0?
  4. Explain why any number raised to the power of zero equals 1.
  5. What is 10210110^2 \cdot 10^{-1}?

Tip:

When multiplying powers with the same base, always remember to add the exponents!

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra

Formulas

a^m · a^n = a^{m+n}
a^0 = 1

Theorems

Zero Exponent Rule

Suitable Grade Level

Grades 6-8