I think you'll have to specify the number of characters you want to limit it to Dale. One can write a much larger number with five characters than with two.

If we limit ourselves to two characters (including arabic numerals and operands like +, -, x, ÷, and !, but exempting ^ for exponentiation since it can be accomplished with superscript), then I think the largest number you can write is 9^9, which is equal to 387420489.

If you allow three characters, I think the largest is (9^9)!, which is equal to 387420489! For the non-math folks out there, that's 1 x 2 x 3 x 4 .... x 387420489.