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

Question

Responses

−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+120)+150=−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(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

Answer 1

To solve the expression \(-4(3 + 12^0) + 15^0\) using the Zero Power Rule, we first need to apply the rule, which states that any non-zero number raised to the power of 0 equals 1.

1. Evaluate the terms with an exponent of 0:

   • \(12^0 = 1\)
   • \(15^0 = 1\)

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

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

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

5. Final calculation: \[ -15 \]

Now looking at the provided responses, the correct sequence showing the steps is:

• Option with correct steps: \[ -4(3+12^0) + 15^0 = -4(3+1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15 \]

Thus, the correct answer corresponds to the third option: \[ -4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15 \]