In an economic unit (like the USA) the employed are paid a wage. That wage is dollars/employed. In our three dimensional world the 3 dimensions are orthogonal. One can move in one direction (say x) but not simultaneously in the other two (y and z). Building or manufacturing something in space requires effort (employed) in each direction (dimension). The cost of such manufacture is the wage rate (i.e employed)*(volume of production, i.e. the product of effort in the x direction * effort in the y direction * effort in the z direction).

Cost therefore is Employed*Employed*Employed*Employed, or Employed^4.
Ergo, GDP=k*Employed^4.