Canonicalization is tough, and requires you to define some common ordering on your units.
Systems will use an array of unit powers, so that if the array were defined as <Joules, Seconds, Newtons, Meters>, then acceleration would be <0,-2,0,1> and watts would be <1,-1,0,0>. Addition and subtraction require that your arrays are equal, and multiplication and division are pairwise additive/subtractive.
Systems will use an array of unit powers, so that if the array were defined as <Joules, Seconds, Newtons, Meters>, then acceleration would be <0,-2,0,1> and watts would be <1,-1,0,0>. Addition and subtraction require that your arrays are equal, and multiplication and division are pairwise additive/subtractive.