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I also noticed something, but am not sure of the reason why. If you find the constants individually for each expression and combine them all, you get a the the power of the number of expressions

e.g.

a ∝ b

a ∝ c

a ∝ d

So the individual constants would be say, k1, k2 and k3 respectively. If you then multiply it all together

a ∝ (k1b)(k2c)(k3d)

You get a^3

If there're expressions, then a^4 etc. All of the numbers I've tried so far have yielded the result but I'm not sure why that's happening

Thanks