Which of the following is developed to result in the answer of 1?(1 point) Responses 50+90 5 superscript 0 baseline plus 9 superscript 0 baseline 3(80) 3 left parenthesis 8 superscript 0 baseline right parenthesis (−2.97)0 left parenthesis negative 2.97 right parenthesis superscript 0 baseline 13−(7.42)0

Question

Which of the following shows the correct process of solving −30+4.5?(1 point) Responses −30+4.5=−3⋅0+4.5=0+4.5=4.5 negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.5 equals 4.5 −30+4.5=−3+4.5=1.5 negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5 −30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5 negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5 −30+4.5=(−3)0+4.5=1+4.5=5.5

Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point) Responses 70+4⋅9 Start Fraction 7 over 0 End Fraction plus 4 times 9 71+4⋅9 Start Fraction 7 over 1 End Fraction plus 4 times 9 75.3+4⋅9 Start Fraction 7 over 5.3 End Fraction plus 4 times 9 75.30+36

Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point) Responses 12(9−0)+0 Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0 12(2)+1 Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1 12(9−1)−1 Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1 12(9−1)+1

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)+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 −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

Answer 1

Here are the responses to each of your questions:

1. Which of the following is developed to result in the answer of 1?
   The answer is 5^0 + 9^0.
   Reason: Any non-zero number raised to the zero power equals 1. So, \( 5^0 = 1 \) and \( 9^0 = 1 \), therefore \( 5^0 + 9^0 = 1 + 1 = 2 \) is incorrect.
   Instead, \( (−2.97)^0 = 1 \), so \( 13 - (7.42)^0 = 13 - 1 = 12 \) is also incorrect.
   However, \( (−2.97)^0 \) gives 1.

2. Which of the following shows the correct process of solving −30 + 4.5?
   The answer is −30 + 4.5 = −3^0 + 4.5 = 0 + 4.5 = 4.5.
   Reason: The expression shows the stepwise breakdown of the operation, correctly applying the zero exponent rule where \( -3^0 = 1 \).

3. Which of the following is an equivalent expression to 7(−5.3)^0 + 4⋅9 when applying the Zero Power Rule?
   The answer is 70 + 4 ⋅ 9.
   Reason: \( (−5.3)^0 = 1 \) implies \( 7 \cdot 1 + 4 \cdot 9 = 7 + 36 = 43 \), but it doesn't directly relate.

4. Which of the following is an equivalent expression to 12(9−70)+(−29)^0?
   The answer is 12(9−0)+0.
   Reason: Here, \( (−29)^0 = 1 \) implies you should consider similar conversions and forms correctly.

5. Which of the following shows the correct process of solving −4(3 + 120) + 150 by generating an equivalent expression using the Zero Power Rule?
   The answer is −4(3 + 12^0) + 15^0 = −4(3 + 1) + 1 = −4⋅4 + 1 = −16 + 1 = −15.
   Reason: It accurately applies the zero power rule at multiple stages to transform, compute, and simplify the expression.

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