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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)
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
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

1 answer

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

  1. Starting with the original expression: \[ -4(3 + 12(0)) + 15(0) \]

  2. Applying the Zero Property: \[ 12(0) = 0 \quad \text{and} \quad 15(0) = 0 \] So this simplifies to: \[ -4(3 + 0) + 0 \]

  3. Thus, it further simplifies to: \[ -4(3) + 0 \]

  4. Now, calculate: \[ -12 + 0 = -12 \]

Now let's look at the options to find the one that applies the Zero Power Rule and follows the calculations correctly.

The option which reflects using the Zero Power and arrives at the correct result seems to be:

−4(3 + 12^0) + 15^0 = −4(3 + 1) + 1 = −4(4) + 1 = −16 + 1 = −15

So the correct response is: −4(3 + 12^0) + 15^0 = −4(3 + 1) + 1 = −4(4) + 1 = −16 + 1 = −15.