A calorie is a unit of heat or energy and it equal about 4.2 J where `1J = 1 kg m^2 s^-2`. Suppose we employ a system of units in which the unit of mass equals `alpha` kg, the unit of length equals `beta` m, the unit of time is `gamma` s. Show that a calorie has a magnitude 4.2 `alpha^-1` `beta^-2` `gamma^2` in terms of the new units.