Question

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

−4(3+12 to the power of 0)+15 to the power of 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+12 to the power of 0)+15 to the power of 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+12 to the power of 0)+15 to the power of 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+12 to the power of 0)+15 to the power of 0=−4(3+1)+1=−4⋅4+1=−16+1=−15

Answer 1

To solve the expression \( -4(3 + 12^0) + 15^0 \) using the Zero Power Rule, we must first understand that any non-zero number raised to the power of 0 equals 1 (i.e., \( a^0 = 1 \) for \( a \neq 0 \)).

1. Applying the Zero Power Rule:
- \( 12^0 = 1 \)
- \( 15^0 = 1 \)

2. Substitute those values into the expression:
\[
-4(3 + 1) + 1
\]

3. Simplify:
- \( 3 + 1 = 4 \)
- \( -4(4) + 1 \)
- \( -16 + 1 = -15 \)

So, the correct process is:
\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15
\]

The response that correctly follows this process is:
**−4(3+12 to the power of 0)+15 to the power of 0=−4(3+1)+1=−4⋅4+1=−16+1=−15**