I'll help you solve these problems. I see several problems involving multiplication and division of numbers in scientific notation. Let's go through them step by step.

I'll start with a few of the problems and work through them. Here's how you handle these operations in scientific notation:

Problem #5:

$(4.0 \times 10^{-2}) \times (2.25 \times 10^{10})$

To solve this:

1. Multiply the coefficients: $4.0 \times 2.25 = 9.0$.
2. Add the exponents of 10: $-2 + 10 = 8$.

So, the answer is: $9.0 \times 10^8$

Problem #6:

$\frac{5.2 \times 10^3}{8.0 \times 10^{-7}}$

To solve this:

1. Divide the coefficients: $\frac{5.2}{8.0} = 0.65$.
2. Subtract the exponents: $3 - (-7) = 10$.

So, the answer is: $0.65 \times 10^{10} \quad \text{or} \quad 6.5 \times 10^9$

I'll continue with these calculations. Would you like more details on specific problems or explanations?