All your numbers are about 10^6, so the only impact is the middle part, 6+6 is 12, 12*324 is 3240+648 which is 3888, the numbers are a bit larger, but you should already know the result is somewhere around 10^4000
This is a pretty rough estimate but usually good enough for daily use.
With this estimate, I can see that you need about 14000 bits to represent the number (or 14 bit exponent in a floating point that cannot represent small numbers).
So a double would not be enough to hold the result, integers could be used, but I really doubt your reasons to why you would chain that many integers together. What was the question again?