https://file.aiquickdraw.com/mathbot/file/1728563962058zdqpz4yn.jpg

The expression provided in the image is:

\[
\frac{6^3 \cdot 6^2}{(6^2)^4}
\]

### Step-by-Step Solution:

1. **Simplify the numerator**:
   - Using the law of exponents \(a^m \cdot a^n = a^{m+n}\), combine the terms in the numerator:
   \[
   6^3 \cdot 6^2 = 6^{3+2} = 6^5
   \]

2. **Simplify the denominator**:
   - Apply the power rule \((a^m)^n = a^{m \cdot n}\) to simplify the denominator:
   \[
   (6^2)^4 = 6^{2 \cdot 4} = 6^8
   \]

3. **Combine the fraction**:
   - Now, rewrite the fraction as:
   \[
   \frac{6^5}{6^8}
   \]
   - Using the quotient rule \( \frac{a^m}{a^n} = a^{m-n} \), subtract the exponents:
   \[
   6^{5-8} = 6^{-3}
   \]

4. **Final Answer**:
   \[
   6^{-3}
   \]

   This can be expressed as:
   \[
   \frac{1}{6^3} = \frac{1}{216}
   \]

The simplified form of the expression is \( \frac{1}{216} \).

Would you like further details or explanations?

### Related Questions:
1. What is the general rule for multiplying exponents with the same base?
2. How do you simplify expressions with negative exponents?
3. Can you explain why \((a^m)^n = a^{m \cdot n}\)?
4. How would you simplify a fraction with variables and exponents?
5. What is the result of \( \frac{a^m}{a^n} \) if \( m < n \)?

**Tip**: Always apply the exponent rules step-by-step to avoid errors in simplification, especially when combining multiple terms with exponents.

Simplify the expression: (6^3 * 6^2) / (6^2)^4

In this solution, we simplify the expression (6^3 * 6^2) / (6^2)^4 using the laws of exponents. This problem focuses on exponent rules and fraction simplification, suitable for students in Grades 8-10.

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