https://file.aiquickdraw.com/mathbot/file/1726190987446efh656ig.jpg

The image shows a math problem from Khan Academy that asks to solve for \( n \) in the equation:

\[
(8^n)^3 = 8^6
\]

### Solution:
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify the left-hand side:

\[
(8^n)^3 = 8^{3n}
\]

Thus, the equation becomes:

\[
8^{3n} = 8^6
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
3n = 6
\]

Now, solve for \( n \):

\[
n = \frac{6}{3} = 2
\]

### Final Answer:
\[
n = 2
\]

Would you like any further explanation or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you simplify expressions like \( (a^m)^n \)?
2. What happens if the equation had been \( (8^n)^3 = 8^9 \)?
3. How do you solve exponent equations when the bases are not the same?
4. Can you explain how exponents and logarithms are related in equations like this?
5. What would change if the equation used a different base, like \( (2^n)^3 = 2^6 \)?

### Tip:
Always look for common bases in exponential equations; it simplifies the process by allowing you to compare exponents directly.

Learn how to solve the exponent equation (8^n)^3 = 8^6 with a detailed step-by-step solution. This problem demonstrates key concepts in exponents, including the laws of exponents and exponent multiplication rule. Suitable for students in Grades 7-9.

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