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

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(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)+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

GPT-4o mini · Answer

To solve the expression $-4(3+120) + 150$ using the Zero Power Rule, we need to note that any non-zero number raised to the power of zero equals 1. Let's examine the options and clarify the corrections: 1. The expression $−4(3+120)+150$ simplifies by first calculating $3 + 120$: - So, $3 + 120 = 123$. - Therefore, the expression becomes $-4(123) + 150 = -492 + 150 = -342$. 2. The options incorrectly involved applying the zero power operation to the number '12' and simply extending it incorrectly to solve the expression. None of the listed options reflect the correct calculations based on simplifying the original expression directly. However, if I had to clarify what the zero power rule implies: - If the expression had originally used powers of zero correctly, it would have been approached differently. - Specifically, using $12^0$ means "1", so that part was correctly made to result in $1$. But then, adjustments on the rest do not line up to unify in solving the expression itself regarding the unique approach being asked with the zero power. Considering the correct stepwise method for visualizing the Zero Power concept mixed in, the closest we can extract from given options might resemble the last two lines showing suppressions of $1$, but are contradictory towards zero understood value. For completeness of correct applicable calculations: The final answer from the expression directly processed should yield a new inspection to clarify the process moving from: $-4(3 + 120) + 150 → -4 \cdot 123 + 150 → -492 + 150 → -342$. Hence, none of the options accurately reflect the correct outcome where -342 should have been.