Math Problem Statement

Simplify to a single power of 6: (6^3)^5

Solution

The expression given in the image is (63)5(6^3)^5, and we are asked to simplify it to a single power of 6.

Using the power of a power property of exponents, which states that (am)n=amn(a^m)^n = a^{m \cdot n}, we can simplify the expression.

(63)5=635=615(6^3)^5 = 6^{3 \cdot 5} = 6^{15}

Thus, the simplified expression is 6156^{15}.

Would you like further clarification or details on this? Here are some related questions:

  1. How do you simplify an expression with multiple exponents?
  2. What is the difference between multiplying powers and raising a power to another power?
  3. How would you evaluate 6156^{15} numerically?
  4. Can you explain the general rules for exponentiation?
  5. How would this expression change if the base was a variable instead of a number?

Tip: When working with exponents, remember that raising a power to another power means you multiply the exponents.

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra

Formulas

(a^m)^n = a^{m \cdot n}

Theorems

Power of a Power Theorem

Suitable Grade Level

Grades 6-8