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The expression you are tasked with simplifying is:

\[
\frac{6n^4}{(3n)(n^8)}
\]

### Step-by-step solution:

1. **Simplify the coefficients**:
   The coefficient in the numerator is 6, and in the denominator is 3. Dividing these gives:
   \[
   \frac{6}{3} = 2
   \]

2. **Simplify the powers of \( n \)**:
   In the numerator, we have \( n^4 \), and in the denominator, we have \( n^1 \times n^8 \). Using the property of exponents \( n^a \times n^b = n^{a+b} \), the denominator becomes:
   \[
   n^1 \times n^8 = n^9
   \]

   Now, we apply the rule for dividing powers with the same base: \( \frac{n^a}{n^b} = n^{a-b} \). So:
   \[
   \frac{n^4}{n^9} = n^{4-9} = n^{-5}
   \]

3. **Final simplified expression**:
   Combining the simplified coefficient and the simplified powers of \( n \), we get:
   \[
   2n^{-5}
   \]

4. **Expressing the answer with positive exponents**:
   Since the problem asks for the answer in terms of positive exponents, we rewrite \( n^{-5} \) as:
   \[
   2 \times \frac{1}{n^5} = \frac{2}{n^5}
   \]

### Final answer:
\[
\frac{2}{n^5}
\]

Would you like further clarification on any step?

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Here are some related questions you can explore:
1. What are the rules for multiplying exponents with the same base?
2. How do you simplify expressions with both coefficients and variables?
3. Can you explain the difference between negative and positive exponents?
4. What happens when you divide powers with the same base but different exponents?
5. How can you convert between different forms of exponential expressions?

**Tip**: When dealing with exponents, remember that multiplying powers with the same base means adding their exponents, and dividing means subtracting them!

Simplify. Express your answer using positive exponents: \[ \frac{6n^4}{(3n)(n^8)} \]

Learn how to simplify the expression \( \frac{6n^4}{(3n)(n^8)} \) using the rules of exponents. This problem involves simplifying both coefficients and powers, including positive and negative exponents, and is suitable for students in Grades 8-10.

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