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)

Question

Responses

−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(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(3+1)+1=−4⋅4+1=−16+1=−15

Answer 1

To clarify the Zero Power Rule: any non-zero number raised to the power of zero equals one (x^0 = 1).

Now let's analyze the expression \(-4(3+120) + 150\):

1. First, we simplify \(3 + 120\): \[ 3 + 120 = 123 \]

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

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

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

However, this does not seem to align with any of the provided options directly.

When considering the options you provided, let’s check them in the light of the Zero Power Rule.

• First Response: \(-4(3 + 120) + 150\) uses \(3 + 120 = 15\) which is incorrect as \(3 + 120 = 123\).

• Second Response: \(-4(3 + 12^0) + 15^0\) is written, but \(12^0 = 1\) and \(15^0 = 1\), thus simplifying gives \(-4(3 + 1) + 1\) which does not follow from the original.

• Third Response: This response shows incorrect calculations from the interpretation of the powers.

• Fourth Response: This attempt too follows incorrectly.

In summary, none of the provided solutions correctly apply the Zero Power Rule or accurately compute the expression \(-4(3 + 120) + 150\) as \(-342\). If we solely focus on using \(x^0 = 1\) and actually substituting in proper values instead of oversimplifying, we should conclude a different equation altogether.

If I had to choose the best answer based on its attempt to apply the Zero Power Rule while realizing mistakes in calculations, it would be the Second Response due to attempting to use \(x^0 = 1\), but again, this option leads to flawed computation.

To answer your original question about which shows the correct process — while none accurately arrive at the solution of the original expression — the most that came close conceptually was based on recognizing \(x^0\) equivalences. Thus, each response ultimately contains errors.