J, 55 4 bytes
^/ .#@# This is literally the definition of tetration.
Usage
f =: ^/ .#@# 3 f 2 16 2 f 1 1 2 f 2 4 2 f 5 3125 4 f 2 65536 Explanation
^/ .#@# Input: b (LHS), a (RHS) # Make b copies of a ^/ .@ Reduce from right-to-left using exponentation