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−45negative 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=−59negative 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=−20negative 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 solve the expression \(-4(3+120)+150\) by generating an equivalent expression using the Zero Power Rule, we can note that any non-zero number raised to the power of zero is equal to 1. This can be applied to the numbers \(12^0\) and \(15^0\):

The correct process would look like this:

1. Recognize that \(120 = 12^1 + 12^0\), so \(12^0 = 1\).
2. So, in the context of the expression, you can replace \(120\) with \(1\) (since \(12^0 = 1\)).
3. This gives \(−4(3 + 1) + 1\).

Carrying out this:

\[ -4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4(4) + 1 = -16 + 1 = -15. \]

Thus, the correct response is:

\(−4(3+12^{0}) + 15^{0} = -4(3+1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15.\)