Question
Negative integer exponents practice
Answers
GPT 3.5
Sure! Here are some practice problems involving negative integer exponents:
1. Simplify: 2^(-3)
Solution: 2^(-3) = 1/2^3 = 1/8
2. Simplify: (4^(-2))^-1
Solution: (4^(-2))^-1 = 4^2 = 16
3. Simplify: 5^(-1) + 3^(-2)
Solution: 5^(-1) + 3^(-2) = 1/5 + 1/9 = 14/45
4. Simplify: (2^(-4))^3
Solution: (2^(-4))^3 = 2^(-12) = 1/2^12 = 1/4096
5. Simplify: (6^(-2)) / (2^(-3))
Solution: (6^(-2)) / (2^(-3)) = 6^(-2+3) = 6^1 = 6
Remember that when simplifying negative exponents, you can either move the base to the denominator or change the sign of the exponent.
1. Simplify: 2^(-3)
Solution: 2^(-3) = 1/2^3 = 1/8
2. Simplify: (4^(-2))^-1
Solution: (4^(-2))^-1 = 4^2 = 16
3. Simplify: 5^(-1) + 3^(-2)
Solution: 5^(-1) + 3^(-2) = 1/5 + 1/9 = 14/45
4. Simplify: (2^(-4))^3
Solution: (2^(-4))^3 = 2^(-12) = 1/2^12 = 1/4096
5. Simplify: (6^(-2)) / (2^(-3))
Solution: (6^(-2)) / (2^(-3)) = 6^(-2+3) = 6^1 = 6
Remember that when simplifying negative exponents, you can either move the base to the denominator or change the sign of the exponent.
sasuke uchiha
1. Yesterday, Sarah spent 35 1/2
minutes studying for a test. Emma spent 1 1/2
times that amount studying for a different test. How many minutes did Emma spend studying?(1 point)
Responses
49 1/2
minutes
49 and 1 halfminutes
5314
minutes
53 1/4
71 minutes
73 1/4
73 1/4
93 1/2
minutes
minutes studying for a test. Emma spent 1 1/2
times that amount studying for a different test. How many minutes did Emma spend studying?(1 point)
Responses
49 1/2
minutes
49 and 1 halfminutes
5314
minutes
53 1/4
71 minutes
73 1/4
73 1/4
93 1/2
minutes
GPT 3.5
To find out how many minutes Emma spent studying, we need to multiply 35 1/2 by 1 1/2.
First, let's convert 35 1/2 into an improper fraction:
35 1/2 = 2 * 35 + 1 = 70 + 1 = 71/2
Next, let's convert 1 1/2 into an improper fraction:
1 1/2 = 2 * 1 + 1 = 2 + 1 = 3/2
Now, we can multiply 71/2 by 3/2:
(71/2) * (3/2) = 213/4 = 53 1/4
Therefore, Emma spent 53 1/4 minutes studying.
First, let's convert 35 1/2 into an improper fraction:
35 1/2 = 2 * 35 + 1 = 70 + 1 = 71/2
Next, let's convert 1 1/2 into an improper fraction:
1 1/2 = 2 * 1 + 1 = 2 + 1 = 3/2
Now, we can multiply 71/2 by 3/2:
(71/2) * (3/2) = 213/4 = 53 1/4
Therefore, Emma spent 53 1/4 minutes studying.
sasuke uchiha
2. A middle school band as 2/9
as many band members as the high school band. The high school band has 502 members. About how many members are in the middle school band?(1 point)
Responses
390
390
112
112
45
45
645
as many band members as the high school band. The high school band has 502 members. About how many members are in the middle school band?(1 point)
Responses
390
390
112
112
45
45
645
GPT 3.5
To find out how many members are in the middle school band, we need to multiply the number of members in the high school band by 2/9.
The number of members in the high school band is given as 502.
So, to find the number of members in the middle school band, we calculate:
502 * (2/9) = 1004/9 ≈ 111.6
Rounding to the nearest whole number, the approximate number of members in the middle school band is 112.
Therefore, there are about 112 members in the middle school band.
The number of members in the high school band is given as 502.
So, to find the number of members in the middle school band, we calculate:
502 * (2/9) = 1004/9 ≈ 111.6
Rounding to the nearest whole number, the approximate number of members in the middle school band is 112.
Therefore, there are about 112 members in the middle school band.
sasuke uchiha
18. Over the past 8 months, Devon made payments for a total of $936 to pay for internet service. The service is the same amount each month. What was the change in Devon’s account each month after paying for the service?(1 point)
Responses
-$936
-$936
$936
$936
-$117
-$117
$117
Responses
-$936
-$936
$936
$936
-$117
-$117
$117
GPT 3.5
To find the change in Devon's account each month, we need to divide the total amount paid by the number of months.
The total amount paid is given as $936 and the number of months is 8.
So, to find the change in Devon's account each month, we calculate:
$936 ÷ 8 = $117
Therefore, the change in Devon's account each month after paying for the service is $117.
The total amount paid is given as $936 and the number of months is 8.
So, to find the change in Devon's account each month, we calculate:
$936 ÷ 8 = $117
Therefore, the change in Devon's account each month after paying for the service is $117.
sasuke uchiha
19. After exposure to an amazing stretching machine, Alexander’s height increased by 108 inches over 6 minutes. His height increased by the same amount each minute. What was the effect on Alexander’s height each minute?(1 point)
Responses
-108 inches
-108 inches
-18 inches
-18 inches
108 inches
108 inches
18 inches
Responses
-108 inches
-108 inches
-18 inches
-18 inches
108 inches
108 inches
18 inches
GPT 3.5
To find the effect on Alexander's height each minute, we need to divide the total increase in height by the number of minutes.
The total increase in height is given as 108 inches and the number of minutes is 6.
So, to find the effect on Alexander's height each minute, we calculate:
108 inches ÷ 6 minutes = 18 inches
Therefore, the effect on Alexander's height each minute after using the stretching machine is 18 inches.
The total increase in height is given as 108 inches and the number of minutes is 6.
So, to find the effect on Alexander's height each minute, we calculate:
108 inches ÷ 6 minutes = 18 inches
Therefore, the effect on Alexander's height each minute after using the stretching machine is 18 inches.