101 zeros.
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10 to the power of 10 to the power of 100 zeros! EDIT: It has 100 zeros. 10^10^100 is a googolplex (10^googol)
the number googol has exactly 100 zeros in it
A googol is 10^100. A googolplex is 10^googol
a googol has 100 zeros.
Seeing as a googol of zeros would be 10^100 zeros, that number of zeros would be quite hard to write out. If you were to try and write out that many zeros by hand at 3 zeros per second, it would still take you 1.05699307 × 1092 years to write them all out.