https://file.aiquickdraw.com/mathbot/file/17263650557116itkvlg5.jpg

The simplified expression is:

\[
\frac{-a^{10}}{5q^{14}}
\]

Would you like more details or have any questions?

Here are five related questions to deepen understanding:

1. How do you simplify exponents when they are raised to another power?
2. What are the rules for combining terms with the same base in the numerator and denominator?
3. How do you deal with negative exponents during simplification?
4. Can you simplify an expression with fractional exponents in a similar way?
5. How would this process change if the bases were different variables?

**Tip:** When simplifying expressions with exponents, always handle powers first, then deal with multiplication and division.

Simplify the expression: -3(q^{-2}a^5)^3 / 15q^8a^5

This problem simplifies an expression with exponents, applying the power rule and negative exponent rules. The step-by-step approach includes handling powers first, then addressing multiplication and division of terms with like bases. Suitable for Grades 9-11.

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