Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−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)+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(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
To generate an equivalent expression using the Zero Power Rule, we need to simplify any expressions with an exponent of zero. Looking at the given options:
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
Here, the Zero Power Rule is not applied correctly. The exponent of zero should make the quantity equal to 1, not the value of the expression itself.
−4(3+120)+150=−4(15)+1=−60+1=−59
In this option, the Zero Power Rule is correctly applied. The quantity (3+1) is replaced by 1, as anything raised to the power of zero equals 1.
Therefore, the correct answer is:
−4(3+120)+150=−4(15)+1=−60+1=−59