1. Which of the following is developed to result in the answer of 1?(1 point)%0D%0AResponses%0D%0A%0D%0A(−2.97)0%0D%0Aleft parenthesis negative 2.97 right parenthesis superscript 0 baseline%0D%0A%0D%0A3(80)%0D%0A3 left parenthesis 8 superscript 0 baseline right parenthesis%0D%0A%0D%0A13−(7.42)0%0D%0A13 minus left parenthesis 7.42 right parenthesis superscript 0 baseline%0D%0A%0D%0A50+90

Question

2. Which of the following shows the correct process of solving −30+4.5 ?(1 point)%0D%0AResponses%0D%0A%0D%0A−30+4.5=(−3)0+4.5=1+4.5=5.5%0D%0Anegative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5%0D%0A%0D%0A−30+4.5=−3+4.5=1.5%0D%0Anegative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5%0D%0A%0D%0A−30+4.5=−3⋅0+4.5=0+4.5=4.5%0D%0Anegative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.5 equals 4.5%0D%0A%0D%0A−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5

3. Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point)%0D%0AResponses%0D%0A%0D%0A75.30+36%0D%0AStart Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36%0D%0A%0D%0A71+4⋅9%0D%0AStart Fraction 7 over 1 End Fraction plus 4 times 9%0D%0A%0D%0A75.3+4⋅9%0D%0AStart Fraction 7 over 5.3 End Fraction plus 4 times 9%0D%0A%0D%0A70+4⋅9

4. Which of the following is an equivalent expression to 12(9−70)+(−29)0 ? (1 point)%0D%0AResponses%0D%0A%0D%0A12(9−0)+0%0D%0AStart Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0%0D%0A%0D%0A12(2)+1%0D%0AStart Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1%0D%0A%0D%0A12(9−1)−1%0D%0AStart Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1%0D%0A%0D%0A12(9−1)+1

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? (1 point)%0D%0AResponses%0D%0A%0D%0A−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20%0D%0Anegative 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%0D%0A%0D%0A−4(3+120)+150=−4(15)+1=−60+1=−59%0D%0Anegative 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%0D%0A%0D%0A−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15%0D%0Anegative 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%0D%0A%0D%0A−4(3+120)+150 =−4(15)+15=−60+15=−45

Answer 1

Here are the correct answers for your questions based on the Zero Power Rule and arithmetic operations:

1. Which of the following is developed to result in the answer of 1?

   • Answer: (−2.97)⁰
   • Explanation: According to the Zero Power Rule, any non-zero number raised to the power of zero equals 1.

2. Which of the following shows the correct process of solving −30+4.5?

   • Answer: −30+4.5=−3⁰+4.5=1+4.5=5.5
   • Explanation: This is the only option that correctly shows the Zero Power Rule being applied (since -3 is equivalent to (-3) raised to the power of 1).

3. Which of the following is an equivalent expression to 7(−5.3)⁰+4·9 when applying the Zero Power Rule?

   • Answer: 71+4·9
   • Explanation: Using the Zero Power Rule, (−5.3)⁰ = 1, so this becomes 7(1) + 4·9.

4. Which of the following is an equivalent expression to 12(9−70)+(−29)⁰?

   • Answer: 12(9−1)+1
   • Explanation: This is correct because (−29)⁰ = 1, thus simplifying the expression correctly.

5. Which of the following shows the correct process of solving −4(3+120)+150 using the Zero Power Rule?

   • Answer: −4(3+120)+150=−4(3+1)+1=−4·4+1=−16+1=−15
   • Explanation: This option correctly applies the Zero Power Rule (12⁰ = 1) and maintains the right arithmetic throughout the equation.

If you have further questions about any of the answers or need additional explanations, feel free to ask!

Answer 2

number 2 is −3^0+4.5=−1⋅3^0+4.5=−1⋅1+4.5=−1+4.5=3.5

Answer 3

Thank you for your patience. Let’s analyze your assertion for Question 2 again.

To solve \(-30 + 4.5\) using the Zero Power Rule:

1. Simplify \(-30\) using the expression: \[ -30 = -3 \times 10 \] Here we can interpret \(-3\) in terms of zero power, but notice that the goal is calculating the sum directly with \(4.5\).

2. Analyzing the old approach:

   • Using the Zero Power Rule: \[ -3^0 + 4.5 = -1 \cdot 3^0 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5 \] This calculation is incorrect because \( -30\) simplifies directly to \( -30 + 4.5\).

3. The correct process should be:

   • \(-30 + 4.5\)
   • That gives: \[ -30 + 4.5 = -25.5 \]

The statement regarding \(-3^0 + 4.5\) resulting in \(3.5\) is indeed incorrect if you look at it through how \( -30 + 4.5\) should directly go. The issue is using the term \(-3^0\) does not accurately represent \(-30\).

Conclusion for Question 2:

None of the options actually computes to \(-30 + 4.5\). If you appreciate using the Zero power method, that transitional calculation can lead to incorrect understanding.

Hence, the statement for “the correct process” using \(-30\) still relies on straightforward arithmetic.

If you have further comments or corrections about my previous conclusions, please let me know!