Math Problem Statement

Simplify the following: (7^2)^2

Solution

To simplify part (72)2(7^2)^2:

Steps:

  1. Apply the power of a power property of exponents: (am)n=amn(a^m)^n = a^{m \cdot n} In this case: (72)2=722=74(7^2)^2 = 7^{2 \cdot 2} = 7^4

  2. Simplify 747^4: 74=7×7×7×7=24017^4 = 7 \times 7 \times 7 \times 7 = 2401

Final Answer:

(72)2=2401(7^2)^2 = 2401

Would you like me to solve other parts or explain this in more detail?

Related Questions:

  1. How do you simplify other nested powers like (33)4(3^3)^4?
  2. What are the steps for evaluating (x3)2(x^3)^2 when x=2x = 2?
  3. How does the rule (am)n=amn(a^m)^n = a^{m \cdot n} apply in general cases?
  4. Can we write (72)2(7^2)^2 as a single multiplication without exponents? How would that look?
  5. Why is it important to simplify nested powers before evaluating?

Tip:

Always simplify exponents step by step to avoid confusion, especially with nested or fractional powers!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponents
Simplification of powers

Formulas

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

Theorems

Power of a power rule

Suitable Grade Level

Grades 6-8