What is the base of the exponent in the function f(x)=3(3\8)^2x when the function is written using only rational numbers and is in simplest form ?

The

by definition, an exponential function with base c is defined by h (x) = ac^x 
where a ≠0, c > 0 , b ≠1, and x is any real number.
The base, c, is a constant and the exponent, x, is a variable. 
so if we have  f(x)=3(3\8)^2x, this equivalent to f(x)=3(3\8)^y(x),
where y (x)=2x, 
therefore, the base is  3/8, and the variable is the function y (x)=2x,