How many zeros in a googolplexplexplexplex?

A googol is 10 to the power of 100, which is a 1 followed by 100 zeros. A googolplex is 10 to the power of a googol, or 10^10^100. A googolplexplex is 10 to the power of a googolplex, or 10^10^(10^100). Adding more "plexes" exponentially increases the number of zeros, so a googolplexplexplexplex would have an incomprehensibly large number of zeros.