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# A calorie is a unit of heat energy and it equals about 4.2 J, where 1 J = 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 and the unit of time is $\gamma$ s. Calorie has a magnitude of ______in terms of the new units.

$\alpha^{-1} \beta^{-2} \gamma^2$