An Expression of Extended Hyper-E is always of the form:
b^a1&(1)a2&(2)...&(n-1)a(n)
where b,a1,a2,...,a(n) are all positive integers and &(1),&(2),...,&(n-1) are "delimiters" of the form #...# where there can be any positive number of consecutive #-marks. For the purposes of definition, '...' may be used to omit a portion of an Extended Hyper-E expression, and & may stand for multiple #-marks. For example '####' may be truncated to &# where & = '###'.
I. Base Law - If there are exactly 2 arguments:
b^p = b to the power of p
II. Termination Law - If the last argument = 1:
b^...y&1 = b^...y
III. Expansion Law - If the last delimiter contains at least 2 '#'s:
b^...y&#z = b^...y&y&#(z-1)
IV. Recursive Law - Otherwise:
b^...y#z = b^...(b^...y#(z-1))
Usage Notes:
If the base (b) is equal to 10, "b^" may be replaced with "E" instead.