I managed to solve it.
I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.) into account to form non-dimensional parameters. Parameter n should also be included, but (since it is non-dimensional) it will not appear anywhere. How can I handle this situation? I am sure that there are other areas in physics where initially known non-dimensional parameters turn up.