My problem is a general one concerning how to best visualize/get a good mental construct for what's happening when we get simple units by multiplying dimensions other than length^2 or length^3. I don't seem to have any trouble with the intuition about the quotient of values: the notion of 'per' suffices pretty well here. I'm going to use MLT for mass, length, time. L/T (velocity) is a ratio comparing how many units of length per unit(s) of time. So here's the crux of it. Say we're talking force with dimensional units of M*L*T^-2. I don't have a problem with per T per T to get T^-2. But how can I visualize what a M*L, like a kg*m is? I've tried thinking about this as a analogous to area being L*L but one of the dimensions is mass, but my visualization breaks down when the units aren't both L. Is there a more illuminating way to think about it, or is a analogy to area going to be as far as I should try to pursue this? Thanks! -_- PS are there any units where we raise units to the power of units? L^T, etc.