Let's solve each question one by one.

Question 9

$\frac{10 \times 10^{-5}}{2 \times 10^{-8}}$

1. Simplify the constants: $\frac{10}{2} = 5$

2. Simplify the powers of 10 using the property $\frac{10^a}{10^b} = 10^{a-b}$: $\frac{10^{-5}}{10^{-8}} = 10^{(-5) - (-8)} = 10^{3}$

3. Combine the results: $5 \times 10^3$

Answer for Question 9: $5 \times 10^3$

Question 10

$\frac{4 \times 10^{-4}}{2 \times 10^{-18}}$

1. Simplify the constants: $\frac{4}{2} = 2$

2. Simplify the powers of 10: $\frac{10^{-4}}{10^{-18}} = 10^{(-4) - (-18)} = 10^{14}$

3. Combine the results: $2 \times 10^{14}$

Answer for Question 10: $2 \times 10^{14}$

Question 11

$\frac{3.51 \times 10^{-2}}{2 \times 10^5}$

1. Simplify the constants: $\frac{3.51}{2} = 1.755$

2. Simplify the powers of 10: $\frac{10^{-2}}{10^5} = 10^{(-2) - 5} = 10^{-7}$

3. Combine the results: $1.755 \times 10^{-7}$

Answer for Question 11: $1.755 \times 10^{-7}$

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

Additional Questions:

1. How would you approach similar problems with different base numbers?
2. What are the properties of exponents that can simplify division and multiplication?
3. How do you handle negative exponents in multiplication or division?
4. Can these types of exponent problems appear in real-world applications?
5. How would adding more variables affect the complexity of these problems?

Tip:

Remember, when dividing powers of 10, simply subtract the exponents: $\frac{10^a}{10^b} = 10^{a-b}$.