Step 1: Factorize $\(1.2 \times 10^{10}\)$
First, let's convert the decimal into a whole number to make it easier to manage:

$$
\(1.2 \times 10^{10}=12 \times 10^9\)
$$


Now, we break these down into their prime components:
- $\(12=2^2 \times 3^1\)$
- $\(10^9=(2 \times 5)^9=2^9 \times 5^9\)$

Combining them:

$$
\(1.2 \times 10^{10}=\left(2^2 \times 3^1\right) \times\left(2^9 \times 5^9\right)=\mathbf{2}^{\mathbf{1 1}} \times \mathbf{3}^{\mathbf{1}} \times \mathbf{5}^{\mathbf{9}}\)
$$

Step 2: Evaluate the Options
For a number to be a divisor, its prime factors must be present in our target number with exponents less than or equal to those in our factorization $\(\left(2^{11}, 3^1, 5^9\right)\)$.
- A. $\(2^{11}\)$ : TRUE. The exponent of 2 is exactly 11 .
- B. 75: TRUE. Since $\(75=3^1 \times 5^2\)$. Both $\(3^1\)$ and $\(5^2\)$ are contained within \($3^1 \times 5^9\)$.
- C. $\(5^{10}\)$ : FALSE. We only have $\(5^9\)$ available. $\(5^{10}\)$ is too large.
- D. 18: FALSE. Since $\(18=2^1 \times 3^2\)$. We only have $\(3^1\)$ available, so we cannot satisfy the $\(3^2\)$ requirement.
- E. $\(3^9\)$ : FALSE. We only have $\(3^1\)$ available.
- F. 36: FALSE. Since $\(36=2^2 \times 3^2\)$. Again, the $\(3^2\)$ makes this impossible as we only have a single 3.

Final Answer:
The divisors of $\(1.2 \times 10^{10}\)$ from this list are:
A. $\(2^{11}\)$ and
B. 75