We are tasked with simplifying the expression:

\[
\frac{8p^9 qr}{2p^4 qr}
\]

### Step-by-Step Simplification:

1. **Simplify the constants**: 
   \[
   \frac{8}{2} = 4
   \]

2. **Simplify the powers of \( p \)**:
   Using the law of exponents \( \frac{p^m}{p^n} = p^{m-n} \), we subtract the exponents of \( p \):
   \[
   \frac{p^9}{p^4} = p^{9-4} = p^5
   \]

3. **Simplify \( q \) and \( r \)**:
   Since \( qr \) appears both in the numerator and the denominator, they cancel out:
   \[
   \frac{qr}{qr} = 1
   \]

### Final Expression:
\[
4p^5
\]

The simplified expression is \( 4p^5 \).

Would you like more details or have any questions?

Here are some related questions to further your understanding:

1. How do you simplify expressions with variables in both numerator and denominator?
2. What happens when dividing two terms with the same exponent but different bases?
3. How do you simplify an expression like \( \frac{12x^8 y^3}{4x^2 y} \)?
4. What are the general rules for canceling out common factors in fractions?
5. Can you explain how to simplify \( \frac{16a^7b}{4a^3b^2} \)?

**Tip**: Always simplify constants and like terms separately to make calculations easier.

Learn how to simplify the algebraic expression 8p^9 qr divided by 2p^4 qr with a detailed step-by-step solution. This problem involves exponent rules and simplifying rational expressions. Perfect for students in Grades 8-10.

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