Final answer:
The base of the exponent in the function f(x)=3(3/8)^2x is 3/8, even when written in simplest rational form.
Step-by-step explanation:
The base of the exponent in the function f(x)=3(\frac{3}{8})^{2x} when the function is written using only rational numbers and is in simplest form is \frac{3}{8}.
To understand the role of the base in an exponential function, it's important to recall that an exponent or a power indicates how many times a base is multiplied by itself. For instance, in the expression 5^2 which equals 25, 5 is the base and is multiplied by itself once because of the exponent 2. This concept of exponents and bases applies to any exponential expression, whether the exponent is an integer, a fraction, or a negative number.
In the case of the function provided, the base is the number which is raised to the power of 2x. Here, that number is \frac{3}{8}. Even when the entire expression is simplified, the base remains unchanged, as simplification typically affects coefficients and exponents but not the base itself. Therefore, the base in its simplest rational number form is still \frac{3}{8}.