If PEs represents the potential energy stored in a spring in kg. m^2 / s2, and x represents the change in spring length from its equilbrium position in m, what is the unitfor the spring constant k in the formula PEs = 1/2 kx^2

We can do dimensional analysis in this particular problem. We do as follows:

PEs = 1/2 kx^2

kg. m^2 / s2 [=] k (m) ²

The units in the left side should be the same units as the resulting units in the right side.

kg. m^2 / s2 [=] (kg/s²) (m) ²

Therefore, the units of k should be kg/s².