To solve the expression $(8.69 \times 10^{-5}) \div (5.5 \times 10^{-7})$, follow these steps:

1. Divide the coefficients:
   $\frac{8.69}{5.5} \approx 1.58$

2. Subtract the exponents:
   $10^{-5} \div 10^{-7} = 10^{-5 - (-7)} = 10^{2}$

3. Combine the results:
   $1.58 \times 10^{2}$

So, $(8.69 \times 10^{-5}) \div (5.5 \times 10^{-7}) \approx 1.58 \times 10^{2}$.

The final answer is $\boxed{158}$.

Would you like more details or have any questions?

Here are some related questions to explore:

1. How do you multiply and divide numbers in scientific notation?
2. What are the rules for adding and subtracting exponents?
3. How does the scientific notation help in simplifying calculations?
4. What are the common mistakes when working with scientific notation?
5. How can you convert a large number into scientific notation?

Tip: Always check the operations on the exponents separately when dealing with scientific notation.