rules for mult, exp, tetr of tetrations

[Matt D]

This has probably been addressed already, but...

we have the rules for exponentiation like

e^x*e^y = e^(x+y) and
(e^x)^y = e^(x*y) and
(e^x)^(e^y) = e^(xe^y)

so for tetration we might expect

(where ^xe means e tetrated to x) (and * means multiplication)

^xe*^ye = ^(x*y)e
^y(^xe) = ^(x^y)e
^(^ye)(^xe) = ^(x^(^ye))e

translated:

e tetrated to x times y tetrated to e = (x times y) tetrated to e

(e tetrated to x) tetrated to y = e tetrated to (x to the y)

(e tetrated to x) tetrated to (e tetrated to y) = e tetrated to (x to the (e tetrated to y))

does this sound reasonable?