Total number of digits in the product of 4^ 1111 * 5^ 2222 is:

The problem can be solved by using the properties of logarithms and the fact that the number of digits in a number is given by the formula: log10(number) + 1.

Step 1: Simplify the expression 4^1111 * 5^2222

4^1111 * 5^2222 = (2^2)^1111 * 5^2222 = 2^2222 * 5^2222 = 10^2222

Step 2: Find the number of digits in 10^2222

The number of digits in a number is given by the formula: log10(number) + 1.

So, the number of digits in 10^2222 = log10(10^2222) + 1 = 2222 + 1 = 2223

So, the total number of digits in the product of 4^1111 * 5^2222 is 2223.