First, I am not a native English-speaking student so I am not good at physics definitions in English. I participated in the MIT e-learning course on classical physics. The 1st lesson is about 3 fundamental physical quantities (time, length and mass).
It mentions dimensional units/quantity and dimensional state. I couldn't find the meaning of those in a dictionary. Can someone give me an specific explanation?
Also, in the lesson, why are the quantities always associated with some power of unknown value like $\alpha,\beta$, etc when we predict the equation? And how do we know what quantities should be added into the equation of a model?