056.js

// 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?

function powerDigitSum(n, power) {
    var digits = [1];
    while (power--) {
        var cr = 0;
        for (var i = 0; i < digits.length; i++) {
            var num = n * digits[i] + cr;
            digits[i] = num % 10;
            cr = Math.floor(num/10);
        }
        while (cr > 0) {
            digits.push(cr % 10);
            cr = Math.floor(cr/10);
        }
    }
    var sum = 0;
    while (digits.length) {
        sum += digits.shift();
    }
    return sum;
}

function maximumDigitalPowerSum(max) {
    var maxsum = 0;
    var n, pow, sum;
    for (n = 1; n < max; n++) {
        for (pow = 1; pow < max; pow++) {
            maxsum = Math.max(maxsum, powerDigitSum(n, pow));
        }
    }
    return maxsum;
}

console.log( maximumDigitalPowerSum(100) );