To solve the expression \(-4(3+120)+150\), we first need to simplify \(120\) using the Zero Power Rule, which states that anything raised to the power of 0 equals 1. Therefore, we can rewrite \(120\) as \(12^0\), which equals \(1\).
So, we can express our original expression as:
\[
-4(3 + 12^0) + 15^0
\]
Now let's evaluate each option based on this understanding.
1. **Option :
\[
-4(3 + 1) + 1 = -4(4) + 1 = -16 + 1 = -15
\]
This option is incorrect because of the final result.
2. **Option B**:
\[
-4(3 + 12^0) + 15^0 = -4(15) + 1 = -60 + 1 = -59
\]
This option is incorrect because \(3 + 1\) does not equal \(15\).
3. **Option C**:
\[
-4(3 + 12^0) + 15^0 = -4(15) + 15 = -60 + 15 = -45
\]
This option is also incorrect since \(3 + 1\) does not equal \(15\).
4. **Option D**:
\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4(4) + 1 = -16 + 1 = -15
\]
This option is correct for the operations but not for the final evaluation as it matches the A option's evaluation.
None of the options lead to the accurate result. However, the correct procedure that applies the Zero Power Rule correctly is shown in **Option A and D** even if A reaches a wrong conclusion.
Thus, when considering which fulfills the criteria to show a correct form of solving the original expression effectively according to their own procedures, **Option D** will be the closest despite discrepancies in the outcomes.