Math Problem Statement

(7^8)^3

Solution

The expression in the image is (78)3(7^8)^3.

To solve this, we apply the power of a power rule in exponents, which states:

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

Here, a=7a = 7, m=8m = 8, and n=3n = 3. Thus, we get:

(78)3=783=724(7^8)^3 = 7^{8 \cdot 3} = 7^{24}

The simplified expression is 7247^{24}.

Would you like further explanation, or do you have any specific questions about this?

Related Questions:

  1. How do you simplify expressions with multiple exponents?
  2. What is the general rule for multiplying powers of the same base?
  3. How would you calculate 7247^{24} using a calculator?
  4. Can you apply this exponent rule to roots as well?
  5. What are some real-world applications of exponential powers?

Tip:

When dealing with multiple powers in an expression, always combine exponents carefully using the laws of exponents to simplify calculations.

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Math Problem Analysis

Mathematical Concepts

Exponents
Laws of Exponents

Formulas

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

Theorems

Power of a Power Rule in Exponents

Suitable Grade Level

Grades 8-10