User blog comment:SuperJedi224/Still Another Generic Function/@comment-5029411-20140213203940

Za,b = Z(b+3a) = 3(3a+b)

Za#b = Z(...Z(a)...) (b Z's)

ZaXb = Za,a...a,a (b a's)

Za##b = Za#a...a#a (b a's)

ZaX*Xb = ZaXa...aXa (b a's)

So Za#^^...^^#b ~ ZaX^^...^^Xb.