octave:39> 10^(0.631570358743543095) * 10^369693099
ans = Inf
running over to WolframAlpha.com
seem like I was wrong originally and they are a little more precise but as close as they will give for free is below which is way more accurate than I can prove.
9^387420489=4.281247731757470480369871159305635213390554822414435 * 10^369693099
Which is way more accurate than I can prove is there a longhand version that some can show with logs? I can probably search for it as well. Trying to use tools and hard head first. But beyond my capabilities to do long hand.
If you don’t have operators it is 999, if you do have operators then it is as big as the operator can become. For example if you make the operators 9!^9!^9! then it will be even bigger than the above answer but you can include even more operators to increase it more like ((((((((((999!)!)!)!)!)!)!)!)!)!) making it become extremely high but you could even create your own operator and do whatever you want with that ex: %* will make any 3 numbers turn into infinity. So then the answer would be %*999.