Nested Cascading-E notation

The Nested cascading-E notation is an extension of Cascading-E notation invented by Aarex Tiaokhiao. It was also called Cascading Hyper-E Notation.

E(a)b = a^b
 * 1) 1 = #
 * 2) n#m = # (# n#m-1)
 * 3) #1m = # #m
 * 4) n #l m = # n #l-1 n...n #l-1 n (m n's)
 * 5) n #^# m = # n #...# m (n #'s)
 * 6) n #^^@ m = n #^#...#^# (@ #^#'s)
 * 7) n #^...^@ m = # n #^...(#^...^@-1) m

The "@" is #^^###...###*# \w 99 #'s.