Units and measurements

A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J =
1 kg m2
s–2. Suppose we employ a system of units in which the unit of mass equals α
kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a
magnitude 4.2 α
–1 β
–2 γ
2
in terms of the new units.