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You can't treat these equations equally, in other words you cant just add an exponent or multiply by one half. If you tried to equate 1/2mv^2 it would look like 1/2pc^2. I see what you're saying because p=mv. However, in the first equation you're squaring velocity, but not squaring mass. You can't square the variable p on the other side because p includes both mass and velocity, you also can't square c because c is a constant, so it wouldn't make sense to. The same thing applies for the 1/2, although it seems logical because p=mv and mv is used in the first equation, because of the difference in values in velocity(v versus v^2) and the addition of the constant, you can't just add the 1/2.
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