Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule?

Question

A.−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15

B. −4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59

C. −4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45

D. −4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20

Answer 1

To solve the expression \(-4(3+120)+150\) correctly, let's first simplify it step by step, using the Zero Power Rule for the term \(120^0\), which is equal to \(1\).

1. Calculate \(120^0\): \[ 120^0 = 1 \]
2. Substitute \(120^0\) into the expression: \[ -4(3 + 120^0) + 150 = -4(3 + 1) + 150 \]
3. Simplify inside the parentheses: \[ -4(4) + 150 \]
4. Multiply: \[ -16 + 150 \]
5. Add: \[ 134 \]

Now let's evaluate the options based on the operations done above:

A:

• Incorrect interpretation; does not simplify correctly.

B:

• Incorrect; it uses incorrect calculations and does not follow the right steps.

C:

• Incorrect; it adds \(15\) but misses key calculations.

D:

• Incorrect as well; does not add the terms correctly.

After evaluating these possible answers based on the step-by-step resolution of the initial expression, it is evident that none of the provided options (A, B, C, D) contain the correct process leading to the answer of \(134\). Therefore, they all show incorrect steps for the original question. The calculations should follow the corrective simplification above.

Answer 2

R u sure

Answer 3

Let's carefully reevaluate the problem and each option again for clarity.

The original expression you want to simplify is:

\[ -4(3 + 120) + 150 \]

Let's break it down step by step:

1. Simplify the parentheses: \[ 3 + 120 = 123 \]

2. Substitute back into the expression: \[ -4(123) + 150 \]

3. Calculate: \[ -4 \times 123 = -492 \] So now you have: \[ -492 + 150 \]

4. Add: \[ -492 + 150 = -342 \]

Now, let's apply the Zero Power Rule context here. \(120^0 = 1\) means that you don't actually have to compute \(120\), but rather just use \(1\) in place of \(120^0\). The expression to solve is \( -4(3 + 1) + 1 \).

This would eventually follow these steps:

1. Substitute: \[ -4(3 + 1) + 1 \] becomes: \[ -4(4) + 1 \]

2. Calculate: \[ -16 + 1 = -15 \]

Now, let's review the provided options using the context of the Zero Power Rule and simplifying \(-4(3+120) + 150\) by interpreting \(120\) as \(120^0\):

• Option A: Incorrect, it produces \(-15\) but incorrectly computes and mixes up powers.

• Option B: Incorrect; makes logical arithmetic errors.

• Option C: Incorrect; does not compute properly and also misuses addition.

• Option D: Incorrect, calculates -20 after an incorrect sequence.

Final verdict: It seems I misunderstood your question context before regarding how the zero exponent applies and is expected in your calculations. When correctly following through with zero exponent logic included, the earlier conclusion of -15 resolves correctly under the provided context of the exercise.

Conclusion: The correct final answer derived from the provided expressions should yield D as the answer, as it follows the aforementioned steps albeit with incorrect final multiplication stemming from the previous wrong steps. However, none of the answers are fully correct on their own, since they apply operations inaccurately.

If you focus specifically on the exponential aspect as per your initial question context, please clarify this part again if needed.