Which of the following is developed to result in the answer of 1?(1 point)
Responses
5^0+9^0
5 superscript 0 baseline plus 9 superscript 0 baseline
3(80)
3 left parenthesis 8 superscript 0 baseline right parenthesis
13−(7.42)^0
13 minus left parenthesis 7.42 right parenthesis superscript 0 baseline
(−2.97)^0
The correct option is 5^0+9^0.
Which of the following shows the correct process of solving −30+4.5?(1 point)
Responses
−30+4.5=(−3)0+4.5=1+4.5=5.5
negative 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
−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=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
The correct option is −30+4.5=−3+4.5=1.5.
Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point)
Responses
75.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
75.30+36
The correct option is 70+4⋅9.
Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point)
Responses
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
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
The correct option is 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(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(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
The correct option is −4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15.
To determine which expression results in the answer of 1, we can calculate each expression and see which one equals 1.
1. 5^0 + 9^0:
To evaluate this expression, we need to understand the exponentiation rules. Any number raised to the power of 0 equals 1. Therefore, both 5^0 and 9^0 equal 1. Therefore, 5^0 + 9^0 equals 1 + 1, which is equal to 2.
2. 3(80):
In this expression, we need to multiply 3 by 80. Multiplying 3 by 80 gives us 240, not 1.
3. 13 - (7.42)^0:
As mentioned before, any number raised to the power of 0 equals 1. Therefore, (7.42)^0 is equal to 1. Then, we subtract 1 from 13, giving us the result of 12.
4. (-2.97)^0:
Once again, as any number raised to the power of 0 equals 1, (-2.97)^0 is equal to 1.
From the given expressions, only (-2.97)^0 results in the answer of 1.