https://file.aiquickdraw.com/mathbot/file/1729882602042nna3cnr3.jpg

The image shows the expression:

\[
25^{12} \cdot 8^8
\]

Let’s simplify it step-by-step.

### Step 1: Rewrite the bases as powers of smaller primes
- \( 25 = 5^2 \), so \( 25^{12} = (5^2)^{12} = 5^{24} \).
- \( 8 = 2^3 \), so \( 8^8 = (2^3)^8 = 2^{24} \).

Thus, the expression becomes:

\[
5^{24} \cdot 2^{24}
\]

### Step 2: Combine the terms
Using the properties of exponents, \( a^m \cdot b^m = (a \cdot b)^m \):

\[
5^{24} \cdot 2^{24} = (5 \cdot 2)^{24} = 10^{24}
\]

### Final Answer:
The simplified expression is:

\[
10^{24}
\]

Would you like more details on any part of the solution?

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Here are 5 related questions you might find helpful:
1. How do you simplify products of exponents with the same power?
2. What are the properties of exponents used in simplification?
3. How do you rewrite larger numbers like 25 and 8 as prime powers?
4. How do exponential expressions behave under multiplication and division?
5. What does \(10^{24}\) represent in scientific notation?

**Tip:** When simplifying exponential expressions, try to express large numbers as prime powers to find patterns.

Learn how to simplify the exponential expression 25^12 * 8^8. This solution involves prime factorization and applying the laws of exponents, resulting in the final answer of 10^24. Suitable for high school students in Grades 9-12.

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