How do you simplify ##lne^4##?

##4##

You may put any power in the argument before the ##ln##: ##lne^4=4lne## (this goes for ##log##'s to any base)

Then since ##e## is the base of the ##ln##-function (##lnx=log_e x##), it follows that: ##lne=log_e e=1##, just as ##log_10 10=1##

So: ##lne^4=4*lne=4*1=4##