If 2^(abc) = 64, where a, b and c are positive integers, what is the value of a + b + c and what is 2^a = 2^b + 2^c?

The first thing we need to do is figure out what power we raise 2 to get 64.
2^2 = 4
2^3 = 8
2^4 = 16
2^5= 32
2^6 = 64

So we know abc = 6 and we know that a,b, and c are different positive integers. So a, b and c must be 1, 2 and 3 in any order since 1*2*3 = 6.

Therefore a + b + c = 6 as well and 2^a + 2^b + 2^c  = 2^1 + 2^2 + 2^3 = 2 + 4 + 8 = 14.

The problem is simply if one knows the rules for exponents and breaks the problem down into steps.