Do you have the exact number for the 8th iteration ?
The script actually calculates strings, then counts the bangbangs. The 7th iteration took about 4 GiB RAM (temporarily, and 2 GiB in the end). Using this approach, I don't think there's enough RAM for the 8th iteration on this planet.
The algorithm would have to be optimized quite a lot before it could calculate the exact 8th value.
168668479408755201
Assuming your approximation "7 Quadrillion" means 7e15 (rather than 7e24 [1]), this is about 24 times as much.
Reason I say this is - let's assume all 159 million bangs are expanded then 159*159 millions = 25 quadrillion
16866847940875521
which is just 2.4 times as much as your approximation.
It would be nice if somebody could confirm my numbers indepdently.
Here is an algorithm for computing them efficiently: https://gist.github.com/robinhouston/6251775