https://file.aiquickdraw.com/mathbot/file/1726092180294g1iy5xw5.jpg

The given expression in the image is:

\[
\left(8^5\right)^6 \cdot 8^2
\]

### Step-by-Step Simplification:

1. **Apply the Power of a Power Rule**: 
   The rule for powers of powers is \(\left(a^m\right)^n = a^{m \cdot n}\). So,
   \[
   \left(8^5\right)^6 = 8^{5 \cdot 6} = 8^{30}
   \]

2. **Combine Powers with the Same Base**:
   When multiplying powers with the same base, the exponents are added: 
   \[
   8^{30} \cdot 8^2 = 8^{30 + 2} = 8^{32}
   \]

Thus, the simplified expression is:

\[
8^{32}
\]

Would you like more details on any part of this explanation?

### Related Questions:
1. What is the power of a product rule in exponents?
2. How can you simplify \((3^4)^2 \cdot 3^5\)?
3. What is the expanded form of \(8^{32}\)?
4. How do you handle negative exponents when simplifying powers?
5. Can you explain the zero exponent rule?

**Tip**: Remember, when multiplying powers of the same base, always add the exponents!

Learn how to simplify the exponential expression (8^5)^6 · 8^2 using the power of a power rule and the product of powers property. This solution explains each step clearly, suitable for students in Grades 8-10.

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