How many zeros are in the number 1googolplex?

First, when dealing with powers of 10 the number of zeros in the number is equal to the power of the 10:

101 = 10 which has 1 zero

102 = 100 which has 2 zeros

103 = 1000 which has 3 zeros

etc.

A googolplex is 10googol

A googlol is 10100 → a googolplex = 10(10100)

→ a googolplex has a googol, or 10100 (which is 1 followed by 100 zeros) zeros. ie a googolplex has 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 zeros