## Powerful digit sum

### Problem 56

Published on Friday, 7th November 2003, 06:00 pm; Solved by 35036; Difficulty rating: 5%A googol (10^{100}) is a massive number: one followed by one-hundred zeros; 100^{100} is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.

Considering natural numbers of the form, *a ^{b}*, where

*a, b*< 100, what is the maximum digital sum?