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To solve this problem, let’s rewrite the equation and simplify it using properties of exponents.

Given:
\[
18^n \cdot 18^8 = (18^4)^6
\]

### Step 1: Simplify the Left Side
Using the property \(a^m \cdot a^n = a^{m+n}\), we can combine the terms on the left:
\[
18^{n + 8}
\]

### Step 2: Simplify the Right Side
Rewrite \((18^4)^6\) using the power of a power property \((a^m)^n = a^{m \cdot n}\):
\[
(18^4)^6 = 18^{4 \cdot 6} = 18^{24}
\]

### Step 3: Set the Exponents Equal
Now that both sides have the base \(18\), we can set the exponents equal to each other:
\[
n + 8 = 24
\]

### Step 4: Solve for \(n\)
\[
n = 24 - 8 = 16
\]

### Conclusion
The value of \(n\) that makes the equation true is:
\[
\boxed{n = 16}
\]

Would you like further clarification on any part of this solution?

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Here are 5 related questions that build on this concept:
1. How would the answer change if the bases in the equation were different?
2. Can we solve a similar problem if the exponent expressions involve variables in the base?
3. How do exponent rules apply when combining terms with different bases?
4. What would happen if one side of the equation had a negative exponent?
5. How does this problem change if the equation involves fractional exponents?

**Tip:** When dealing with exponents, always look for ways to simplify terms by applying properties like \((a^m)^n = a^{m \cdot n}\) and \(a^m \cdot a^n = a^{m+n}\).

Which value of n makes the equation 18^n * 18^8 = (18^4)^6 true?

Learn how to find the value of n that makes the equation 18^n * 18^8 = (18^4)^6 true. This step-by-step solution covers key concepts like properties of exponents, including the power and product rules, making it ideal for students in Grades 8-10.

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