What is the rate of increase for the function f(x)=1/3 (^3√24)^2x

You need to simplify the function first until the exponent turns into a plain x. step 1 leave 1/3 alone that is the a value, initial value. you are looking for the base

step 2 deal with the parenthesis. factor 24 and you will get 2 and the cube of 3. 

step 3 separate the exponent (2) (x)

step 4 now square each term inside the parenthesis
2 squared and cube of 3 square  the 2^2 will be 4, the other expression means  cube of 3 times cube of 3 and that's cube of 9

step 5 your base should be (4 cube of 9)