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

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

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..

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1 answer
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Answer 1

Bot GPT 4-o mini answered
27 days ago

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.