How to pick what unit to display a value in?

Question

I have a value and I known that it's units is

meters^(mn/md) * kg^(kn/kd) * s^(sn/sd) * K^(Kn/Kd) * A^(An/Ad)

Note: the exponents are rational, units of m^0.5 are valid

The question is how to pick how to break down the units into something more compact

for instance if

md=kd=sd=Kd=Ad=1
mn=Kn=An=0
kn=1
sn=-1

I can use N/m

I suspect that this is some subset of a discreet optimization problem.

Answer 1

Define the complexity as the total number of symbols: A unit to the power of 1 has complexity 1, any other integer power is 2, a fractional power is 3. Try several examples and see how it feels. Maybe you have to use other numbers than 1, 2, 3 for complexities.

Try optimization using a greedy algorithm: on each iteration, factor out the composite unit (possibly to a fractional or negative power) that simplifies as much as possible (makes the target function as small as possible). I have a hunch that greed will work because the units are designed so that if the product / ratio of two units is simpler than each of them, it will be a unit of its own.