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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(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=−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 −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

1 answer

To solve the expression −4(3+120)+150 by using the Zero Power Rule, we first recognize that any non-zero number raised to the power of zero is equal to 1.

In this context:

  • \( 12^0 = 1 \)
  • \( 15^0 = 1 \)

Now, let's break down the expression step by step using the Zero Power Rule.

The first option presented is:

  • \( −4(3+120)+150 = −4(15)+1 = −60+1 = −59 \)

This can be translated using the Zero Power Rule as:

  • \( −4(3 + 12^0) + 15^0 = −4(3 + 1) + 1 = −4(4) + 1 = −16 + 1 = −15 \) (This step is incorrect).

The second option presented is:

  • \( −4(3+120)+150 = −4(3+1)+1 = −4(4)+1 = −16+1 = −15 \) (This step is correct).

The third option presented is:

  • \( −4(3+120)+150 = −4(15)+15 = −60+15 = −45 \) (This step does not use the Zero Power Rule correctly).

The fourth option presented is:

  • \( −4(3+120)+150 = −4(3+1)+1 = −4(4)+1 = −4(5) = −20 \) (This step does not conclude correctly either).

Conclusion:

The correct option representing the process is:

  • Second Option: \( −4(3+120)+150 = −4(3+1)+1 = −4(4)+1 = −16+1 = −15 \)

This option shows the correct application of the Zero Power Rule correctly and leads to a correct expression simplification.