Question

Which of the following shows the correct process of solving −4(3+12 to the power of 0) +15 to toe power of 0
by generating an equivalent expression using the Zero Power Rule? (1 point)
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(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)+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+12 tp the power of 0) +150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20

Answer 1

To solve the expression \(-4(3 + 12^0) + 15^0\) using the Zero Power Rule, we first recognize that any non-zero number raised to the power of 0 equals 1. Therefore, we have:

\[
12^0 = 1 \quad \text{and} \quad 15^0 = 1
\]

Now substituting these values into the expression:

\[
-4(3 + 1) + 1
\]

Now we simplify the expression step by step:

1. Simplify inside the parentheses:
\[
3 + 1 = 4
\]

2. Then we have:
\[
-4(4) + 1
\]

3. Performing the multiplication:
\[
-16 + 1
\]

4. Finally, we add:
\[
-16 + 1 = -15
\]

Thus, the correct equivalent expression generation process is:

\[
−4(3 + 12^0) + 15^0 = −4(3 + 1) + 1 = −4 \cdot 4 + 1 = −16 + 1 = −15
\]

So the correct answer is:

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