How much is 1,(one-hundred zeros) to the 1,(one-hundred zeros)th power???

Question

You know how google means 1 followed by one hundred zeos, then what is a google to the googleth power?

Answer 1

The answer is:
10^10^100

This has been given the name "googolplex"

Googol can be expanded to:
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

But there are too many zeroes for me to list the full decimal expansion of googolplex.

Best I can say is:
10^googol
or
10^10 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000

This is 1 followed by a *googol* zeroes.

Edit:
Yes, the name of the search engine (Google) is a play on the number (googol). And their headquarters (Googleplex) is a play on this even larger number (googolplex).

And before you ask, some people have already coined the terms googolplexplex, googolplexplexplex, etc. for 10^googolplex, 10^googolplexplex, etc.

Edit2:

Correction, I have indeed answered the question for 10^googol. Since you asked about googol^googol, what you really want is:

(10^100)^(10^100)

This can be rewritten as:
10^10^100^100

This is googolplex^100

Can we just say "really big" and leave it at that? Or do we have to mention that Graham's number would make this number pale in comparison?

Answer 2

Puzzling is right

From Wikipedia:

The Googleplex is the company headquarters for Google, Inc., located at 1600 Amphitheatre Parkway in Mountain View, Santa Clara County, California, near San Jose.

The name Googleplex is a play on words, being a combination of the words Google and complex, and a reference to googolplex, the name given to the large number 10^10^100.

Hope that helps.

Answer 3

The correct answer is 10^(100googol). Perhaps the easiest way to see this is to realize that if we take the common log of googol^googol we get the number of zeroes following the one in our number. But log(googol^googol) = googol(log googol) = 100(googol), and the correct answer follows at once. Clearly, this is not googolplex as others have erroneously stated, but rather googolplex^100. Tourists!