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)+15=−60+15=−45
−
4
(
3
+
12
0
)
+
15
0

=
−
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=−4⋅5=−20
−
4
(
3
+
12
0
)
+
15
0
=
−
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)+1=−60+1=−59
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
15
)
+
1
=
−
60
+
1
=
−
59
negative 4 left parenthe…

Answer 1

To solve the expression \(-4(3+120)+150\) using the Zero Power Rule, we need to understand that \(12^0 = 1\).

Here’s the step-by-step breakdown with the correct response:

1. Start with the original expression:
\[
-4(3 + 120) + 150
\]

2. Apply the Zero Power Rule, knowing that \(120 = 12^0 = 1\):
\[
-4(3 + 1) + 1
\]

3. Simplify inside the parentheses:
\[
-4(4) + 1
\]

4. Multiply:
\[
-16 + 1
\]

5. Finally, add:
\[
-15
\]

Thus, the equivalent expression using the Zero Power Rule is:
\[
-4(3+1) + 1 = -16 + 1 = -15
\]

However, note that this did not reach the final answer correctly in your options as per the calculations shown.

Among your options, the correct sequence is:
\(-4(3+120)+150 = -4(15)+15 = -60+15 = -45\)

Thus, the response:
\[
\text{-4(3 + 12^0) + 15^0 = -4(15) + 15 = -60 + 15 = -45}
\]
is the correct process expressing the calculations to reach \( -45\).