Zero Power Rule of Exponents Quick Check
1 of 51 of 5 Items
Question
Which of the following is developed to result in the answer of 1?(1 point)
Responses
13−(7.42)0
13 minus left parenthesis 7.42 right parenthesis 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
50+90
The correct answer is (3(80)). When any non-zero number is raised to the power of 0, the result is always 1.
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)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+4.5=1.5
The correct answer is −30+4.5=−3+4.5=1.5. To solve the expression, we add the values -30 and 4.5 to get the result of 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
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
Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36
75.3+4⋅9
The correct answer is 75.3+4⋅9. When applying the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. Therefore, 7(-5.3)^0 simplifies to 7(1) which is equal to 7. Since 4 times 9 is 36, the final expression becomes 75.3 + 36.
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 plus 1
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
The correct answer is 12(9−0)+0. When any number is subtracted by 0, the result is that number itself. Therefore, 9 minus 0 is equal to 9. Additionally, any number raised to the power of 0 is equal to 1. Thus, (-29)^0 simplifies to 1. Therefore, the given expression becomes 12(9) + 0, which can be further simplified to 12(9) or 12 times 9.
Which of the following is an equivalent expression to 1/2(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 plus 1
1/2(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
1/2(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
1/2(2)+1
The correct answer is 1/2(9−0)+0. When any number is subtracted by 0, the result is that number itself. Therefore, 9 minus 0 is equal to 9. Additionally, any number raised to the power of 0 is equal to 1. In this case, (-29)^0 equals 1.
Thus, the given expression becomes 1/2(9) + 0, which further simplifies to 1/2 times 9 or 9/2.
To find the expression that results in the answer of 1, we need to look for an expression with a base raised to the power of 0.
Let's examine each provided expression:
1. 13 - (7.42)^0: This expression involves subtraction and does not have a base raised to the power of 0.
2. 3 * 8^0: This expression involves multiplication and has a base of 8 raised to the power of 0. Any number (except 0) raised to the power of 0 is equal to 1. Therefore, this expression results in 1.
3. (-2.97)^0: This expression involves a negative number raised to the power of 0. Similarly, any non-zero number raised to the power of 0 is equal to 1. Therefore, this expression also results in 1.
4. 50 + 90: This expression involves addition and does not have a base raised to the power of 0.
So, the expressions that result in the answer of 1 are:
- 3 * 8^0
- (-2.97)^0.