Math Problem Statement

Simplify to a single power of 5: (5^2)^6

Solution

The expression in the image is:

(52)6(5^2)^6

To simplify this, you can apply the rule of exponents that states (am)n=am×n(a^m)^n = a^{m \times n}. Here, the base a=5a = 5, the exponent m=2m = 2, and n=6n = 6. Using the rule:

(52)6=52×6=512(5^2)^6 = 5^{2 \times 6} = 5^{12}

So, the simplified expression is:

5125^{12}

Would you like any further clarification or have any other questions? Here are some related topics you might find interesting:

  1. How do you multiply two powers with the same base?
  2. What are other properties of exponents?
  3. How do you handle negative exponents?
  4. How do fractional exponents work?
  5. Can you explain why exponents follow these specific rules?

Tip: When simplifying powers of a power, remember to multiply the exponents!

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Math Problem Analysis

Mathematical Concepts

Exponents
Simplification of powers

Formulas

(a^m)^n = a^(m * n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 6-8