$$10^{10^{100}}$$
When you evaluate power towers like this, always do the exponentiation from the "deepest level" first, that is, from the top of the tower in the notation:
$$10^{10^{100}} = 10^{(10^{100})}$$
We know that:
a^b = a*a*a*a* ... *a*a*a*a with b number of a's
So it logically follows that 10^100 must contain 100 number of 0's. With other words, we know that 10^100 is a number containing a one followed by 100 zeros:
10^100 = 1000000... ...00000 with 100 number of 0's
So it logically follows that the original number, 10^10^100, must be the number containing a one followed by a number of 0's equal to the number represented by a one followed by 100 zeros. ( I bet you had to read the last sentence twice ;) )
So indeed 10^10^100 is a large number, but it ain't nothin' compared to infinity.
Always to help well im going to bed cause im going to see the statu of liberty 
