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ACT Exam  >  ACT Questions  >  If, a, b, and c are positive integers such th... Start Learning for Free
If, a, b, and c are positive integers such that ab = m and c2b = n, then mn =?
  • a)
    (ac2)b
  • b)
    (ac)3b
  • c)
    2(ac)b
  • d)
    ac2b
  • e)
    abc
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If, a, b, and c are positive integers such that ab = m and c2b = n, th...
If ab = m and c2b = n, then mn = (ab) (c2b). Because a and c are not necessarily the same number, you cannot simply add the exponents. The only legitimate answer choice that further manipulates the expression (ab) (c2b) factors out the b exponent and places it outside a set of parentheses. Thus (ab) (c2b) = (abc2b) = (ac2)b.
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A physicist performs a series of experiments to determine the relative magnitude of electric charge on four particles. A given particle is considered to have a higher magnitude of charge than another if it will push out (or draw in) a positive test charge farther than the other particle.A particle that pushes the test charge has positive charge, while a particle that pulls (or draws in) the test charge has negative charge. This is known as the sign of the charge. Magnitude of charge is unrelated to sign.The experiment is conducted on a horizontal axis that measures from 20m in total: from –10m on the left to +10m on the right, with a measurement of 0m in the middle.Experiment 1Particle A is placed at position –5m on the horizontal axis. The test charge has a specific magnitude of charge and is located at +3m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.Experiment 2Particle B is placed at position –8m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at 0m on that same axis. The result of the experiment is that the test charge is displaced to –7.5m.Experiment 3Particle C is placed at position 0m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +8m on that same axis. The result of the experiment is that the test charge is displaced to +10m.Experiment 4Particle D is placed at position –5.5m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +2.5m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.Q.If particle C and particle D are placed on the axis at the same time, accoring to the results of the experiment, what is likely to occur?

In a physics class, students conducted a series of experiments by placing different objects into a beaker of water. They conducted twenty trials for each object. For each trial, they recorded whether or not the object floated.First, they placed a steel paper clip into the water. They observed that the paper clip usually sank; however, they also saw that occasionally, the paper clip stayed afloat if it was placed very gently on top of the water. Next, they repeated the the same procedure using a cork, a toy boat made of aluminum, and a glass marble. They observed that both the cork and the toy boat always stayed afloat in the water, but that the glass marble always sank.Below, three students give their explanations for these observations.Student 1:Objects float when they are less dense than the liquid in which they are immersed. For example, when immiscible liquids of varying densities are mixed together in a container, the most dense liquid will sink to the bottom of the container, while the least dense liquid will rise to the top. This same principle applies to solid objects. Because the cork and the aluminum toy boat always float, cork and the aluminum of the boat must be less dense than water. Because the glass marble always sinks, the glass of the marble must be more dense than water.Objects that are more dense than water can also float due to surface tension. Surface tension occurs because molecules of a liquid are more attracted to each other more than they are to other objects. Molecules on the surface of water are attracted to the molecules around them and below them. This attraction causes a liquids surface to behave if it were covered by a thin film, which resists penetration by other objects. Therefore, small objects such as paper clips can sometimes float on water when the upward force of waters surface tension exceeds the force of gravity pulling such objects down. Because the paper clips often sink and only float sometimes, we can conclude that they are indeed more dense than water, and that their floating is due to surface tension.Student 2:Objects float in two different cases: when they are buoyed by a liquids surface tension or when their average density is less than that of the liquid in which they are immersed. The average density of cork is less than that of water. This is why the cork floats. In contrast, the density of glass is more than that of water. This is why the glass marble sinks.However, the densities of aluminum and of steel are greater than that of water. Thus, density cannot be used to explain why the aluminum toy boat and the paper clip float. Both of these objects float because of surface tension. Because the paper clip does not have much mass, the normal upward force created by waters surface tension can be enough to allow it to float. Other objects with greater mass, like the toy boat, employ a particular shape to magnify the force of surface tension. The curved shape of the boats bottom both stabilizes the boat and increases the amount of the boats surface area that touches the water, maximizing the force due to surface tension that the boat receives.Student 3:In this experiment, the paper clip floats because of surface tension; however, the cork, toy boat, and marble float or sink because of their relationship to a buoyant force. All objects immersed in a liquid experience a buoyant force, which pushes them upward. The strength of this force is equal to the weight of the liquid displaced, or pushed aside, by an object. Every object also experiences a downward force due to gravity, which is measured as the objects weight, and which is directly proportional to the objects mass. When the buoyant force acting on an object is greater than the downward force due to gravity, the object floats. However, when the buoyant force is less than the force due to gravity, the object sinks. Both the cork and the aluminum toy boat are able to displace enough water to create a buoyant force that exceeds the force due to gravity, so they float. However, the glass marble does not displace enough water to create a sufficient buoyant force, so it sinks.Q.Paint is more dense than cooking oil; however, when a drop of paint is dripped into a container of cooking oil, it floats on top of the oil. If Student 1s explanation is correct, which of the following is most likely the reason for this observation?

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If, a, b, and c are positive integers such that ab = m and c2b = n, then mn =?a)(ac2)bb)(ac)3bc)2(ac)bd)ac2be)abcCorrect answer is option 'A'. Can you explain this answer?
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