I would argue that 9^9 mentioned in the article for example _is not a number_. It is a method for calculating a number. So most of the article is invalid
So is 387420489. The method goes, first you take 9, then you multiply 8 by 10 and add that to 9, then you multiply 4 by 100 and add that to what you have...
You're probably viewing it as a programmer. You see the exponentiation operator, which to you means "computation", which implies some "work" must occur to get the "real" number out of the calculation.
As far as a mathematician is concerned, there is no difference between 9^9, 387420489, 387420499 - 10, 774840978 / 2, or 193710244.5 * 2. They all represent the same quantity. That some are not in their fully reduced form does not change that they are unambiguous representations of the same number.
Even if you are unable to see it that way, we can easily rephrase the exercise to be "write down a way to compute the largest number you can in 15 seconds". This is an enlightening mental exercise, it would be silly to dismiss it for such trivial reasons.
