https://file.aiquickdraw.com/mathbot/file/1728877118251bl3vioa9.jpg

The expression provided in the image is:

\[
\frac{2^5 \cdot 2^3}{2^2 \cdot 2^4}
\]

To simplify this, let's follow the rules of exponents:

1. Combine the exponents in the numerator and the denominator:
   - In the numerator: \( 2^5 \cdot 2^3 = 2^{5+3} = 2^8 \).
   - In the denominator: \( 2^2 \cdot 2^4 = 2^{2+4} = 2^6 \).

2. Now, simplify the fraction:
   \[
   \frac{2^8}{2^6} = 2^{8-6} = 2^2
   \]

3. Calculate \( 2^2 \):
   \[
   2^2 = 4
   \]

So, the simplified result is \( 4 \).

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you multiply powers with the same base?
2. What is the rule for dividing powers with the same base?
3. How would the result change if the exponents in the numerator and denominator were different?
4. What happens if the base numbers are different in such expressions?
5. How do negative exponents affect such calculations?

**Tip:** When multiplying powers with the same base, you add their exponents; when dividing, you subtract the exponents.

Simplify the expression \(\frac{2^5 \cdot 2^3}{2^2 \cdot 2^4}\).

Learn how to simplify the expression \(\frac{2^5 \cdot 2^3}{2^2 \cdot 2^4}\) using the laws of exponents. This problem involves multiplying and dividing powers, and is suitable for students in Grades 6-8.

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