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(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 −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 Skip to navigation

Answer 1

To solve the expression −4(3 + 120) + 150 using the Zero Power Rule where \(x^0 = 1\) for any non-zero \(x\), we first notice that \(120\) can be expressed as \(12^0 = 1\).

Thus, the expression can be rewritten as follows:

\[ −4(3 + 12^0) + 15^0 \]

Now let's break it down step by step:

1. Replace \(12^0\) with \(1\): \[ −4(3 + 1) + 1 \]

2. Simplify inside the parentheses: \[ −4(4) + 1 \]

3. Multiply: \[ −16 + 1 \]

4. Finally, add: \[ −15 \]

Thus, the expression simplifies to \(−15\).

Therefore, the correct response that goes through this process is:

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.