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Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses

−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

−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

−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

−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
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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To solve the expression \( -4(3 + 120) + 150 \) while applying the Zero Power Rule, we need to note that any non-zero number raised to the power of 0 is 1. However, in this case, the original question requires us to handle the problem as it stands without relying on misinterpretations of the numbers involved.

Let's examine the provided options:

1. **Option 1**:
\(-4(3 + 120) + 150 = -4(15) + 1 = -60 + 1 = -59\)

The reasoning here does not properly apply the Zero Power Rule, as it improperly suggests \( 120^0 = 1 \), but it's not relevant to the expression as written.

2. **Option 2**:
\(-4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15\)

This does not correctly apply the arithmetic for \( 120 \) nor utilize the Zero Power Rule accurately, and does simplistically assume values which are logically incorrect.

3. **Option 3**:
\(-4(3 + 120) + 150 = -4(15) + 15 = -60 + 15 = -45\)

While the math here is correct, it does not mention or include any Zero Power Rule.

4. **Option 4**:
\(-4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15\)

Similar to Option 2, this misinterprets values and does not correctly apply the Zero Power Rule.

Given all the responses do not effectively demonstrate the Zero Power Rule within a legitimate setup, it appears none of the options precisely adhere to the requirement set forth in your question.

However, Option 1 results in the correct final expression mathematically, despite the inaccuracies regarding \(0\) power references. Therefore, the interpretation error doesn't hinder the arithmetic progression substantially. Thus, it can be concluded but remains unclear if this was indeed the right perspective toward finding a solution aligned with your request.

So the closest valid option if we neglect the Zero Power Rule oversight would be the first, yielding an arithmetic conclusion albeit incorrectly engaging with the rule itself. Would you like to clear up any potential misunderstandings or delve further into the Zero Power Rule?