How many many zeros does googolplex have?

A googol has 100 zeros.

A googolplex has a googol of zero

No, a googolplex has 10 x 100 googols.

NO, a googolplex is 10 to the 10th to the 100th. There are so many zeroes in a googolplex, if you wrote a zero on every atom in the universe, it still wouldn't be enough 0s