a more interesting challenge would be the biggest number using each of the ten digits only once.
ready, go.
ready, go.
Somehow I think that Conway's chained arrow notation is cheating.
Then again 2^3^4^5^6^7^8^9^(10!!!!!!!!!) is larger. Also if it's it's simply a question of symbols 9!! is larger than 9^9 so 9 followed by n ! is probably your best bet without going into higher level math like BB(BB(...(9))...)
If I'm also allowed an operator, 3↑⁹⁸⁷⁶⁵⁴¹⁰2
That would be trivial to increase substantially by using some other notation for the hyperoperation, but I'm going with the presumably most familiar one. I'm sure there are bigger numbers - specifically, Wikipedia mentions Conway chains, where a→b→c = a ↑^c b, and so 2→3→4→5→6→7→8→9→10 should be quite large indeed.