Which quantities have the same dimensions?

Different quantities can share their dimensions. You will make the program build the dimensions of seven quantities from their formulas, and then group together the ones that match.

The idea. A dimension is three powers $(\text{M}, \text{L}, \text{T})$. Multiplying two quantities adds their powers; dividing subtracts them.

Your tasks.

1. Build the dimensions of force ($ma$), work ($Fs$) and torque ($F \times$ distance).
2. Build pressure ($F/A$), energy per volume, and power ($W/t$).
3. Collect the names into groups that share the same dimensions.