The expression you provided is:

\[
\frac{p^6 \cdot r + p^5}{q^3}
\]

There is no common factor to simplify this expression further. It is already in its simplest form unless additional constraints or values are provided.

Would you like a deeper explanation or have any questions?

Here are 5 related questions to explore further:

1. How would you simplify \(\frac{p^7 + p^6 \cdot r}{q^2}\)?
2. Can you factor any terms in the numerator of \(\frac{p^6 + p^5 \cdot r}{q^3}\)?
3. How would the expression change if \(r = 0\)?
4. What would happen if \(q = 1\)? How would the expression simplify?
5. Can you differentiate \(\frac{p^6 \cdot r + p^5}{q^3}\) with respect to \(p\)?

**Tip**: When working with algebraic expressions, always check for common factors in the numerator and denominator to potentially simplify the equation.

Explore the simplification of the algebraic expression (p^6*r + p^5) / q^3. Learn key concepts in algebra, including exponent rules and the structure of rational expressions. Suitable for students in Grades 9-11.

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