# Problem statement
* A googol ($10^{100}$) is a massive number, i.e., one followed by one hundred zeros.
* $100^{100}$ ($10^{200}$) is almost unimaginably large, i.e., 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 'ab,' where a, b < 100, what is the maximum digital sum?*

# Expected output
```C
Maximum digital sum = 972
```

# Solution
Let's look at the code snippet below. It gives a solution for how to calculate the powerful digital sum of a, b < 100.

a = 100
b = 100
maxSum = 0
for i in range(a):
    for j in range(b):
        temp = i**j #i**j = i^j
        temp = map(int, str(temp)) #mapping int to string as it is less costly to parse strings than dealing with big integers
        sumList = list(temp) #making a list of numbers

        tempSum = sum(sumList); #calculating sum of digits
        if(tempSum > maxSum):
            maxSum = tempSum #finding max sum
print "Maximum digital sum = ", maxSum

# Explanation
The nested loop calculates the exponent $i^{j}$, where 0<i<100 and 0<j<100. The sum of the digits of the exponent is calculated in *line 10* and the maximum digit sum is stored in `maxSum` in *line 12*. This is the *powerful digital sum* $a^{b}$ for a<100 and b<100.

How to calculate the powerful digital sum

Natural numbers $a^b$ where $a, b < 100$ yield a maximum digital sum of 972.