https://file.aiquickdraw.com/mathbot/file/1730638830061l4b8fn7q.jpg

The expression in the image is:

\[
\left( \frac{3 \cdot 2^2 \cdot 2^5}{8 \cdot 3^2} \right)^3 \cdot \left( \frac{2 \cdot 3^5 \cdot 2^2}{3^3 \cdot 2^8} \right)^2
\]

To simplify, we can break it down step-by-step.

1. **Simplify each fraction inside the parentheses** by combining like terms.
2. **Apply the exponents** to each part of the simplified fraction.
3. **Combine the results** by multiplying.

Would you like a detailed breakdown of these steps? 

Here are some questions that expand on this:

1. How do we handle exponents when simplifying expressions like this?
2. What are common rules for working with powers in fractions?
3. Can we cancel out terms before applying the exponents?
4. How do we combine terms with the same base?
5. What happens if any terms reduce to 1?

**Tip:** Always simplify the fraction inside the parentheses before applying the outer exponent; it saves time and reduces calculation complexity.

Simplify the expression \( \left( \frac{3 \cdot 2^2 \cdot 2^5}{8 \cdot 3^2} \right)^3 \cdot \left( \frac{2 \cdot 3^5 \cdot 2^2}{3^3 \cdot 2^8} \right)^2 \)

Learn how to simplify the expression \( \left( \frac{3 \cdot 2^2 \cdot 2^5}{8 \cdot 3^2} \right)^3 \cdot \left( \frac{2 \cdot 3^5 \cdot 2^2}{3^3 \cdot 2^8} \right)^2 \) using exponent rules and fraction simplification. This problem covers key mathematical concepts, including the power of a power, multiplication and division of exponents, and simplification strategies. Suitable for students in Grades 8-10.

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