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We are tasked with finding the value of \( n \) that satisfies the equation:

\[
8^n = 8^9 \cdot 8^3
\]

### Step 1: Apply the property of exponents
We know that when multiplying numbers with the same base, we add the exponents:

\[
8^9 \cdot 8^3 = 8^{9+3} = 8^{12}
\]

### Step 2: Set the equation equal
Now, the equation becomes:

\[
8^n = 8^{12}
\]

### Step 3: Equate the exponents
Since the bases are the same, we can set the exponents equal to each other:

\[
n = 12
\]

Thus, the value of \( n \) is \( \boxed{12} \).

Would you like more details on how the exponent rules work or have any further questions?

Here are some related questions you may find interesting:
1. What happens when we divide terms with the same base in exponents?
2. How can we simplify exponential equations with different bases?
3. What is the general rule for multiplying powers with the same base?
4. How would this problem change if the equation involved division instead of multiplication?
5. Can this method be applied to logarithmic equations as well?

**Tip:** When working with exponents, remember that multiplying powers with the same base means adding the exponents!

Enter the value of n that makes the equation 8^n = 8^9 ⋅ 8^3 true.

Find the value of n in the equation 8^n = 8^9 ⋅ 8^3 by using properties of exponents. This step-by-step solution demonstrates how to combine exponents and equate them, suitable for students in Grades 7-9.

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