For n variable there is 2^2^n means here for 2^2^3=256
but acc. to question-
f(x,y,z)=f(x′,y′,z′), means output should be same for (0,0,0)and (1,1,1), (0,0,1)) and (1,1,0)(1,1,0) and so on total 4 groups .
So, We have four input cases (pairs) for which output can be 00 or 11. So, we have two cases for each pair.
Total functions possible =2^4=16