To simplify the expression $\frac{a^{-13}}{a^{-6}}$ and rewrite it in the form $a^n$, let's use the properties of exponents.

Step-by-Step Solution:

1. When dividing powers with the same base, we subtract the exponents: $\frac{a^{-13}}{a^{-6}} = a^{-13 - (-6)}$

2. Simplify the exponent by removing the double negative: $a^{-13 + 6} = a^{-7}$

Final Answer:

$\frac{a^{-13}}{a^{-6}} = a^{-7}$

Would you like a further breakdown, or do you have any questions?

Related Questions:

1. How would you simplify $\frac{a^{-8}}{a^{3}}$?
2. What is the result of $a^5 \cdot a^{-2}$?
3. How do you simplify $(a^{-3})^4$?
4. What is the value of $a^0$ for any nonzero $a$?
5. How can you simplify $\frac{b^3}{b^{-5}}$?

Tip:

When dividing terms with the same base, remember to subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.