User blog comment:Deedlit11/Is BEAF well-defined?/@comment-5150073-20121023091257

I guess that:

Line of exponential space has "length":

Length 1 = X (or 1 dimensional array) = X^^1

Length 2 = X^X (or 1 superdimensional array) = X^^2

Length 3 = X^(X^X) (or 1 trimensional array) = X^^3

Length 4 = X^(X^(X^X)) (or 1 quadramensional array) = X^^4

Exponential space which has any length = X^^X

Next structures might be (X^^X)^2 (plane of exponential spaces)

(X^^X)^3 (realm of exponential spaces)

(X^^X)^X (1 superdimension of exponential spaces)

(X^^X)^2X (2 superdimensions of exponential spaces)

(X^^X)^(X^2) (superdimension of superdimensions of exponential spaces)

As for 3^10 & 3, this is X^10 structure, because "array of" & symbol has lowest precedence.