Use the Product Rule of Exponents to simplify the expression 2 with the exponent of 4 ⋅2 with the exponent of 2.
To find out how long it will take Rubio to get to his friend's house, we need to determine the number of intervals of 2/3 mile he needs to cover.
Given that his friend's house is 1 mile away, we need to find the number of intervals of 2/3 mile that equal 1 mile.
1 ÷ (2/3) = 1 * (3/2) = 3/2 = 1.5 intervals
Since each interval takes 16 minutes according to the given information, Rubio will need to multiply the number of intervals by 16 to find the total time:
1.5 intervals * 16 minutes/interval = 24 minutes
Therefore, it will take Rubio 24 minutes to get to his friend's house.
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To simplify the expression 2^4 ⋅ 2^2 using the Product Rule of Exponents, we add the exponents together because the bases are the same.
2^4 ⋅ 2^2 = 2^(4+2) = 2^6
Therefore, the simplified expression is 2^6.
Use the product rule of exponents to simplify the expression 3^8 3^3
To simplify the expression 3^8 ⋅ 3^3 using the Product Rule of Exponents, we add the exponents together because the bases are the same.
3^8 ⋅ 3^3 = 3^(8+3) = 3^11
Therefore, the simplified expression is 3^11.
Use the Product Rule of Exponents to simplify the expression 7^5 ⋅7^2.
To simplify the expression 7^5 ⋅ 7^2 using the Product Rule of Exponents, we add the exponents together because the bases are the same.
7^5 ⋅ 7^2 = 7^(5+2) = 7^7
Therefore, the simplified expression is 7^7.
Use the Product Rule of Exponents to simplify the expression 7^2 ⋅7^3.
To simplify the expression 7^2 ⋅ 7^3 using the Product Rule of Exponents, we add the exponents together because the bases are the same.
7^2 ⋅ 7^3 = 7^(2+3) = 7^5
Therefore, the simplified expression is 7^5.
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Apologies for the mistake. To simplify the expression 7^2 ⋅ 7^3 using the Product Rule of Exponents, we add the exponents together because the bases are the same.
7^2 ⋅ 7^3 = 7^(2+3) = 7^5
Therefore, the simplified expression is 7^5.
Find the numerical equivalent of 7^2⋅7^3
To find the numerical equivalent of 7^2 ⋅ 7^3, we can simply perform the multiplication of 7^2 and 7^3.
7^2 is equal to 7 * 7 = 49.
7^3 is equal to 7 * 7 * 7 = 343.
Now, we can multiply these two values together:
49 * 343 = 16807.
Therefore, the numerical equivalent of 7^2 ⋅ 7^3 is 16807.
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Find the numerical equivalent of 3^9⋅3^−5
To find the numerical equivalent of 3^9 ⋅ 3^-5, we can simplify each exponent and then multiply the resulting values.
First, simplify the exponents:
3^9 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 19683
3^-5 = 1 / (3^5) = 1 / (3 * 3 * 3 * 3 * 3) = 1 / 243
Now, multiply the simplified values:
19683 * (1 / 243) = 81
Therefore, the numerical equivalent of 3^9 ⋅ 3^-5 is 81.
Rubio decides he is going to walk to his friend's house, which is 1 mile from his house. He can walk at a pace of 2/3
mile in 16 minutes. At this rate, how long will it take him to get to his friend’s house?
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
327
32 superscript 7 baseline
62⋅73
6 squared times 7 cubed
108⋅108
The expression correctly developed to use the Product Rule of Exponents is:
(5^2)^9
This means that 5 squared is raised to the power of 9.
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Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10056
100 superscript 56 baseline
20015
200 superscript 15 baseline
10,00015
10,000 superscript 15 baseline
10015
The correct answer is:
10015
The expression 1008⋅1007 is simplified using the Product Rule of Exponents by adding the exponents together because the bases are the same. In this case, the base is 10, and the exponents are 8 and 7.
Therefore, the simplified expression is 10^15.
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
1,100
1,100
105
10 superscript 5 baseline
10
10
100,000
To find the numerical equivalent of 102 ⋅ 103, we simply perform the multiplication of 10^2 and 10^3.
10^2 = 10 * 10 = 100
10^3 = 10 * 10 * 10 = 1000
Now, we can multiply these two values together:
100 * 1000 = 100,000
Therefore, the numerical equivalent of 102 ⋅ 103 is 100,000.
Find the numerical equivalent of 25 ⋅2−2(1 point)
Responses
8
8
16
16
128
128
2
To find the numerical equivalent of 25 ⋅ 2^(-2), we can simplify the expression first and then calculate the value.
2^(-2) is equivalent to 1 / (2^2) = 1/4.
Now, we can multiply 25 and 1/4:
25 * 1/4 = 25/4 = 6.25
Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 6.25.
Bot, whats the quotient of 1/2 and 12/7 ?
To find the quotient of 1/2 divided by 12/7, we can multiply the first fraction by the reciprocal of the second fraction.
1/2 ÷ 12/7 is the same as 1/2 * 7/12.
Now, we can multiply the numerators and denominators:
(1 * 7) / (2 * 12) = 7/24
Therefore, the quotient of 1/2 and 12/7 is 7/24.
Find the numerical equivalent of 2^5 ⋅2−2(1 point)
Responses
8
8
16
16
128
128
2
To find the numerical equivalent of 2^5 ⋅ 2^(-2), we can simplify the expression first and then calculate the value.
2^5 is equal to 2 * 2 * 2 * 2 * 2, which equals 32.
2^(-2) is equivalent to 1 / (2^2), which is 1/4.
Now, we can multiply 32 and 1/4:
32 * 1/4 = 32/4 = 8
Therefore, the numerical equivalent of 2^5 ⋅ 2^(-2) is 8.
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Find the numerical equivalent of 4^9⋅4^(−7)(1 point)
Responses
4
4
42
4 squared
16
16
416
4 superscript 16 baseline
To find the numerical equivalent of 4^9 ⋅ 4^(-7), we can simplify the expression first and then calculate the value.
4^9 is equal to 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4, which equals 262,144.
4^(-7) is equivalent to 1 / (4^7), which is 1/16,384.
Now, we can multiply 262,144 and 1/16,384:
262,144 * 1/16,384 = 262,144/16,384 = 16
Therefore, the numerical equivalent of 4^9 ⋅ 4^(-7) is 16.
A ball bounces on the ground. How do the ball and the ground act on each other?(1 point)
Responses
The ball and the ground exert forces on each other with equal magnitude but in opposite directions.
The ball and the ground exert forces on each other with equal magnitude but in opposite directions.
The ball and the ground exert forces on each other with equal magnitude and in the same direction.
The ball and the ground exert forces on each other with equal magnitude and in the same direction.
The ball exerts a stronger force than the ground and in the opposite direction.
The ball exerts a stronger force than the ground and in the opposite direction.
The ball exerts a stronger force than the ground but in the same direction.
The ball and the ground exert forces on each other with equal magnitude but in opposite directions.
According to Newton’s third law of motion, which statement is always correct?(1 point)
Responses
If a moving object hits another object, then the second object will start moving.
If a moving object hits another object, then the second object will start moving.
If a moving object hits another object, then the second object will push back.
If a moving object hits another object, then the second object will push back.
If two moving objects collide, then they will bounce off each other.
If two moving objects collide, then they will bounce off each other.
If two moving objects collide, then both will stop moving.
According to Newton's third law of motion, the statement that is always correct is:
If two moving objects collide, then they will bounce off each other.
Newton's third law states that for every action, there is an equal and opposite reaction. In the case of two objects colliding, the force exerted by one object on the other will result in an equal and opposite force exerted by the second object on the first. This is what causes the objects to bounce off each other.
Two metal balls with the same mass hang so that they are touching each other. The ball on the left is pulled to the side and released. What will happen when it swings back and hits the ball on the right?(1 point)
a. Both balls will swing to the left.
b. The ball on the right will swing to the right.
c. Both balls will swing to the right.
d. The ball on the left will stop, and the ball on the right will remain still.
When the ball on the left is pulled to the side and released, it will swing towards the right and collide with the ball on the right. According to Newton's third law of motion, for every action, there is an equal and opposite reaction.
So, when the ball on the left hits the ball on the right, the ball on the right will experience a force in the opposite direction equal to the force exerted by the ball on the left.
Therefore, the correct answer is:
c. Both balls will swing to the right.
How do bumper cars at an amusement park demonstrate Newton’s third law?(1 point)
a. If two bumper cars collide with a certain force, then one car will transfer its force to the other car and they will move together in the same direction.
b. If two bumper cars collide with a certain force, then they will move away from each other in opposite directions with a stronger force.
c. If two bumper cars collide with a certain force, then one car will transfer its force to the other car and they will move away from each other in opposite directions.
d. If two bumper cars collide with a certain force, then they will move away from each other in opposite directions with the same force.
The correct answer is:
c. If two bumper cars collide with a certain force, then one car will transfer its force to the other car, and they will move away from each other in opposite directions.
This is an example of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. When the bumper cars collide, they exert equal and opposite forces on each other. As a result, one car transfers its force to the other car, causing them to move away from each other in opposite directions.
An octopus propels itself through the water by ejecting water through a funnel in its body. How does this demonstrate Newton’s third law?(1 point)
a. When the octopus ejects the water out, the water acts with an equal force on the octopus in the same direction.
b. When the octopus ejects the water out, the water acts with an equal force on the surrounding water in the same direction.
c. When the octopus ejects the water out, the water acts with an equal force on the surrounding water in the opposite direction.
d. When the octopus ejects the water out, the water acts with an equal force on the octopus in the opposite direction.
The correct answer is:
c. When the octopus ejects the water out, the water acts with an equal force on the surrounding water in the opposite direction.
This demonstrates Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. When the octopus propels itself by ejecting water through a funnel, the force exerted by the water on the surrounding water is equal in magnitude but opposite in direction to the force exerted by the octopus on the water. This action-reaction pair allows the octopus to move forward in the water.