Largest Integer Expressible by 3 Digits

Theorem
The largest integer that can be represented using no more than $3$ digits, with no additional symbols, is:
 * $9^{9^9} = 9^{387 \, 420 \, 489}$

and (at $369 \, 693 \, 100$ digits, is too large to be calculated on a conventional calculator.

Note that this does not include the notation for tetration: ${}^9 9$.