To simplify the expression $\frac{1}{3}^9 \div \frac{1}{3}^5$, you can apply the laws of exponents.

Step-by-Step Solution:

1. Use the Quotient Rule of Exponents:
   The quotient rule states that: $\frac{a^m}{a^n} = a^{m-n}$ Applying this to your expression: $\frac{(1/3)^9}{(1/3)^5} = \left(\frac{1}{3}\right)^{9-5} = \left(\frac{1}{3}\right)^4$

2. Simplify $\left(\frac{1}{3}\right)^4$:
   This means: $\left(\frac{1}{3}\right)^4 = \frac{1^4}{3^4} = \frac{1}{81}$

Final Answer:

$\frac{1}{3}^9 \div \frac{1}{3}^5 = \frac{1}{81}$

Would you like more details or have any questions about this?

Here are 5 related questions:

1. What is the Quotient Rule of Exponents?
2. How would you simplify $\left(\frac{1}{2}\right)^7 \div \left(\frac{1}{2}\right)^3$?
3. What happens when the exponents are the same in a division problem like $\frac{a^m}{a^m}$?
4. Can you simplify $\left( \frac{2}{3} \right)^4 \div \left( \frac{2}{3} \right)^2$?
5. What is the rule for simplifying powers of negative numbers?

Tip: Always subtract the exponents when dividing powers with the same base!