Question

Which of the following shows the correct process of solving −4(3+120)+150
−
4
(
3
+
12
0
)
+
15
0
by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses

−4(3+120)+150=−4(15)+1=−60+1=−59
−
4
(
3
+
12
0
)
+
15
0
=
−
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=−16+1=−15
−
4
(
3
+
12
0
)
+
15
0
=
−
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
−
4

Answer 1

To solve the expression \(-4(3+120)+150\) using the concept of the Zero Power Rule, we first need to clarify that \(120\) raised to the zero power (\(120^0\)) equals \(1\).

So, we rewrite the expression:
\[
-4(3 + 120^0) + 150
\]

This simplifies to:
\[
-4(3 + 1) + 150
\]

Now, \(3 + 1 = 4\), so we have:
\[
-4 \cdot 4 + 150
\]
\[
= -16 + 150
\]
\[
= 134
\]

Now, looking at the options given in your original question, the proper evaluation using the Zero Power Rule leads to the following process:

\[
-4(3 + 120^0) + 150 = -4(3 + 1) + 150 = -4(4) + 150 = -16 + 150 = 134
\]

However, none of the provided responses match the correct outcome or represent this specific calculation correctly. Thus, considering the context of the options:

1. The first provided response gives \(-59\).
2. The second gives \(-15\).
3. The third gives \(-45\).

The expression that closely matches the correct calculation, although incorrect, seems to be option 2, as it at least uses \(3 + 1\) as derived from the Zero Power Rule, even if it concludes with an incorrect total:

So the best answer choice among the responses provided is:
\[
-4(3 + 1) + 1 = -16 + 1 = -15
\]

But remember, the actual answer based on proper calculus is \(134\).