9^(9^9)

A very large number.

To get an approximation:

9⁹ = 387,420,489

So,  9^{(9^9)}  =  9^{387 420 489}

Let  x  be equal to 9^{387 420 489}    

--->   x  =  9^{387 420 489}    

Now, take the log of both sides:

--->     log[ x ]  =  log[ 9^{387 420 489}  ]

Since an exponent in a log expression comes out as a multiplier:

--->     log[ x ]  =  387,420,489 · log[ 9 ]

--->     log[ x ]  =  369 693 099 .6    (approximately)

Solving for x by rewriting the log as an exponential expression:

--->     x  =  10^{369 693 099 .6}         (approximately)

What is 9^(9^9)?

It's a very large number consisting of 369,693,100 digits long!!. If you were to write it down in a straight line with each digit 1 meter apart, it would go all the way from here to the moon(almost)!.