One practical use case is for dimensional analysis. A type is then a k-tuple of type-level integers where k is the number of primitive units, e.g. (kg, m, s). Then m^2 / kg would be the tuple (-1, 2, 0). Multiplying two quantities adds the tuples elementwise. For example multiplying the above type by a quantity of type kg / m / s (corresponding to (1, -1, -1)) would give (0, 1 -1), which is the correct m / s.

Addition would only be allowed if the types are equal.