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?

I just took the test and the answer is 4.

The answer:

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,