To simplify the expression \(\frac{5p^{-7}}{20p^2}\), follow these steps:

1. **Simplify the Coefficients**: 
   \[
   \frac{5}{20} = \frac{1}{4}
   \]
   So the expression becomes:
   \[
   \frac{1}{4} \cdot \frac{p^{-7}}{p^2}
   \]

2. **Apply the Laws of Exponents**:
   Use the rule \(\frac{a^m}{a^n} = a^{m-n}\):
   \[
   \frac{p^{-7}}{p^2} = p^{-7-2} = p^{-9}
   \]

3. **Final Expression**:
   Combine the results:
   \[
   \frac{1}{4} \cdot p^{-9} = \frac{1}{4p^9}
   \]

So, the simplified form of the expression is:
\[
\frac{1}{4p^9}
\]

Would you like further details on any of these steps, or have any questions?

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Here are 5 related questions to expand on this:

1. How would you simplify \(\frac{8x^{-3}}{16x^4}\)?
2. What is the general rule for multiplying exponents with the same base?
3. Can you simplify \(\frac{10p^5}{2p^{-3}}\)?
4. How do you simplify an expression like \(a^m \cdot a^n\)?
5. What happens when you have a negative exponent in the denominator?

**Tip**: Always simplify coefficients first before handling the variables with exponents.

Learn how to simplify the algebraic expression 5p^-7/20p^2 step-by-step by applying exponent rules and fraction simplification. This solution covers key concepts in algebra and is suitable for students in Grades 7-9.

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