Powerful Digit Sum

Problem Statement

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?

Approach

The solution involves:

1. Iterating through all combinations where a < 100 and b < 100
2. Computing a^b using BigInteger to handle large numbers
3. Converting each result to a string and summing its digits
4. Tracking the maximum digit sum found