https://file.aiquickdraw.com/mathbot/file/17255882317151xn6p5vj.jpg

The given expression from the image is:

\[
\frac{(2^3)^2 \cdot 3^2}{3^3 \cdot 2^4}
\]

Let's simplify this step by step:

1. Simplify the terms:
   \[
   (2^3)^2 = 2^{3 \cdot 2} = 2^6
   \]
   So the expression becomes:
   \[
   \frac{2^6 \cdot 3^2}{3^3 \cdot 2^4}
   \]

2. Now, apply the properties of exponents (i.e., subtract exponents when dividing terms with the same base):
   - For \(2\): \( \frac{2^6}{2^4} = 2^{6-4} = 2^2 \)
   - For \(3\): \( \frac{3^2}{3^3} = 3^{2-3} = 3^{-1} \)

3. The expression now becomes:
   \[
   2^2 \cdot 3^{-1}
   \]
   Which is:
   \[
   \frac{2^2}{3} = \frac{4}{3}
   \]

Thus, the simplified result of the given expression is:

\[
\frac{4}{3}
\]

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

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

This problem involves simplifying an exponent expression using exponent rules. Learn how to simplify (2^3)^2 * 3^2 / (3^3 * 2^4) step-by-step by applying the power of a power rule and the quotient rule for exponents. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation