It makes more sense for 2^3^4 = 2^(3^4). If you meant (2^3)^4, then it would be more efficient to calculate 2^(3*4), because exponentiation takes much longer than multiplication.

On a related note, in Excel, -1^2 = 1 because they are calculating (-1)^2 instead of the more standard interpretation, -(1^2).