Let's solve the given expression:

$\frac{(3.2 \times 10^{10})(3.75 \times 10^6)}{(4 \times 10^6)(6 \times 10^5)}$

Step 1: Multiply the numbers in the numerator and denominator separately.

Numerator: $(3.2 \times 10^{10}) \times (3.75 \times 10^6) = (3.2 \times 3.75) \times 10^{10+6} = 12 \times 10^{16}$

Denominator: $(4 \times 10^6) \times (6 \times 10^5) = (4 \times 6) \times 10^{6+5} = 24 \times 10^{11}$

Step 2: Divide the results.

$\frac{12 \times 10^{16}}{24 \times 10^{11}} = \frac{12}{24} \times 10^{16-11} = 0.5 \times 10^5$

Step 3: Adjust to proper scientific notation.

Since $0.5$ is not in standard form, we convert it: $0.5 \times 10^5 = 5.0 \times 10^4$

Thus, the answer is $5.0 \times 10^4$, which corresponds to option C.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you handle multiplication of numbers in scientific notation?
2. What happens when the base number in scientific notation is not between 1 and 10?
3. How can you simplify large numbers using scientific notation?
4. What are the rules for adding and subtracting exponents when multiplying and dividing powers of 10?
5. Why is it necessary to convert the final answer into proper scientific notation?

Tip: Always check if the result needs to be adjusted into proper scientific notation, with the coefficient between 1 and 10!