To simplify the expression $\frac{9a^{-5}}{3a^{5}}$, follow these steps:

1. Simplify the coefficients: $\frac{9}{3} = 3$

2. Combine the powers of $a$ using the property $a^m \div a^n = a^{m-n}$: $a^{-5} \div a^{5} = a^{-5-5} = a^{-10}$

Putting it all together, we get: $\frac{9a^{-5}}{3a^{5}} = 3a^{-10}$

This can also be expressed as: $\frac{3}{a^{10}}$

Would you like more details or have any questions? Here are some related questions:

1. How can I simplify expressions with negative exponents further?
2. What are the rules for multiplying and dividing exponents?
3. How do you convert negative exponents to positive exponents?
4. Can you give examples of similar expressions?
5. What is the significance of exponents in algebra?

Tip: Remember that any term with a negative exponent can be rewritten as a fraction.