The calorie is a unit of heat or energy and it equals about 4.2 J where `1J=1kgm^(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. Show that the calorie has a magnitude of `4.2alpha^(-1) beta^(-2) gamma^(2)` in terms of the new units.

Explanation

To solve the problem, we need to express the calorie in terms of a new system of units defined by mass, length, and time. The steps are as follows:

### Step 1: Understand the given information
We know that:
- 1 calorie = 4.2 joules
- 1 joule = 1 kg·m²/s²

### Step 2: Write the dimensional formula for energy
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