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For the equation Ek = (1/2)m*v^2, the ^2 only applies to v (v^2). If we take a look at the units this make sense. Kinetic energy is given in the units of Joules (J), which translates to kg*m^2*s^-2. Thus, when looking at the units of the equation (1/2)m*v^2 we get kg*m^2*s^-2. If we were to square the entire thing we would get kg^2*m^2*s^-2, which are not the correct units. Hope this helps!
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