Higher Powers

Write a program that determine the largest possible value of

a^b - b^c + c^a

...where a, b and c are each distinct positive integers and that the product of the three values is 16.

Your program should output the values of a, b, and c as well as the output of the formula, similar to:

The values of a, b, and c are {}, {}, and {} and the answer is {}.

(Inspiration for this challenge is from http://www.cemc.uwaterloo.ca/resources/potw.php)