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Let's break down the given expression:

\[
\frac{6x^{-20}}{x^{-30}}
\]

### Step-by-Step Solution:

1. **Simplify the exponents:**
   The variable part involves dividing powers of the same base \(x\). Using the exponent rule:
   \[
   \frac{x^a}{x^b} = x^{a-b}
   \]
   We subtract the exponents:
   \[
   x^{-20 - (-30)} = x^{-20 + 30} = x^{10}
   \]

2. **Final expression:**
   Now the simplified form of the expression is:
   \[
   6x^{10}
   \]

So, the simplified result is:

\[
6x^{10}
\]

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Would you like further clarification or additional details on this problem?

### Related Questions:
1. How do you apply the rules of exponents in division for negative powers?
2. What happens when both exponents are negative, and how does subtraction work in that case?
3. How would the expression change if it was \(\frac{6x^{-20}}{x^{30}}\) instead?
4. How can you simplify expressions involving fractional exponents?
5. What are some other exponent rules that are useful in simplifying complex expressions?

**Tip:** Always be cautious when handling negative exponents; remember they indicate reciprocals, and proper application of the exponent rules will simplify the problem.

Learn how to simplify the expression 6x^{-20} / x^{-30} using the rules of exponents. This solution covers the subtraction of exponents when dividing like bases and the proper handling of negative exponents. Suitable for students in Grades 9-11.

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