Math Problem Statement

Simplify the following expression: (2^3)^2 * 3^2 / (3^3 * 2^4)

Solution

The given expression from the image is:

(23)2323324\frac{(2^3)^2 \cdot 3^2}{3^3 \cdot 2^4}

Let's simplify this step by step:

  1. Simplify the terms: (23)2=232=26(2^3)^2 = 2^{3 \cdot 2} = 2^6 So the expression becomes: 26323324\frac{2^6 \cdot 3^2}{3^3 \cdot 2^4}

  2. Now, apply the properties of exponents (i.e., subtract exponents when dividing terms with the same base):

    • For 22: 2624=264=22\frac{2^6}{2^4} = 2^{6-4} = 2^2
    • For 33: 3233=323=31\frac{3^2}{3^3} = 3^{2-3} = 3^{-1}
  3. The expression now becomes: 22312^2 \cdot 3^{-1} Which is: 223=43\frac{2^2}{3} = \frac{4}{3}

Thus, the simplified result of the given expression is:

43\frac{4}{3}

Would you like more details on any part of this solution? Here are 5 related questions for further exploration:

  1. How do exponent rules work when multiplying or dividing terms with the same

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra

Formulas

Power of a power rule: (a^m)^n = a^(m*n)
Quotient rule for exponents: a^m / a^n = a^(m-n)

Theorems

Exponent Rules

Suitable Grade Level

Grades 7-9