To solve \(\dfrac{a^{-13}}{a^{-6}}\), we can apply the property of exponents that states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

In this case, \(m = -13\) and \(n = -6\). So, we subtract the exponents:

\[
a^{-13 - (-6)} = a^{-13 + 6} = a^{-7}
\]

Thus, the simplified expression is:

\[
\frac{a^{-13}}{a^{-6}} = a^{-7}
\]

Would you like more details on the steps or have any questions?

Here are five related questions:

1. How would you simplify \(\frac{a^{-3}}{a^{-8}}\)?
2. What is the result of \(\frac{b^{5}}{b^{-2}}\)?
3. Simplify \(\frac{x^{7}}{x^{2}}\).
4. How would you express \(a^{-7}\) as a fraction?
5. What is the simplified form of \(\frac{y^{0}}{y^{-5}}\)?

**Tip:** When dealing with exponents, remember that subtracting a negative exponent is equivalent to adding its positive counterpart.

Explore how to simplify the algebraic expression \dfrac{a^{-13}}{a^{-6}} using the rules of exponents. This step-by-step solution covers key concepts in algebra, specifically working with negative exponents. Ideal for students in Grades 8-10.

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