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(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 −4(3+120)+150=−4(15)+1=−60+1=−59

Answer 1

Let's analyze the expression \( -4(3 + 120) + 150 \).

1. First, simplify the expression inside the parentheses: \[ 3 + 120 = 123 \]

   Now we rewrite the expression: \[ -4(123) + 150 \]

2. Next, multiply: \[ -4 \times 123 = -492 \]

3. Finally, add 150: \[ -492 + 150 = -342 \]

Now, comparing this with the responses given, it appears that none directly reaches the calculation of the original expression \( -4(3 + 120) + 150 \) correctly using the Zero Power Rule or a simplified calculation.

However, using the Zero Power Rule, which states that any non-zero number raised to the power of 0 is 1 (i.e., \( a^0 = 1 \)), we can correctly interpret \( 12^0 \) and \( 15^0 \) as 1. When applied, this would lead us to simplify \( 3 + 120 \) as \( 3 + 1 \) and \( 150 \) as \( 1 \), but that seems conceptually incorrect as they should equal their numerical values.

Let’s check each response:

1. Response 1: \( -4(3 + 1) + 1 \) This incorrectly applies the Zero Power Rule; it simplifies incorrectly.

2. Response 2: \( -4(15) + 15 = -60 + 15 = -45 \) The calculation here seems mistaken in its handling of the inputs.

3. Response 3: Similar errors in simplifications lead to incorrect results.

4. Response 4: This leads to \( -60 + 1 = -59 \), which is also incorrect.

Since all responses contain mistakes or misinterpretations, the correct procedure to solve \( -4(3 + 120) + 150 \) does not match any of the provided options clearly.

Thus, I would conclude that none of the responses correctly demonstrate the correct process to solve the expression \( -4(3 + 120) + 150 \).