A beautiful Olympiads Exponential Trick | No Calculator Allowed 📵

[@BollyFan2-ue6cq]

If you are going to calculate it manually, then there is a much more easier and straight forward way to do it:
9^2 = 81
9^4 = 81^2 = (80 + 1)^2 = 80^2 + 2*80*1 + 1^2 = 6400 + 160 + 1 = 6561
9^8 = 6561^2 = 6561 * 6 * 1000 + 6561 * 5 * 100 + 6561 * 6 * 10 + 6561 * 1 * 1
9^8 = 39366 * 1000 + 32805 * 100 + 39366 * 10 + 6561
9^9 - 99 = 9 * (9^8 - 11) = 9 * (39366 * 1000 + 32805 * 100 + 39366 * 10 + 6561 - 11)
= 9 * (39,366,000 + 3,280,500 + 393,660 + 6,550)
= 9 * x
where
x = 39,366,000
+ 3,280,500
+ 393,660
+ 6,550
_________________
= 43,046,710
9^9 - 99 = 9 * 43,046,710 = 387,420,390

[@subasu478]

11

[@RealQinnMalloryu4]

3^3^3^3 ➖ 3^3^3^3 1^1^1^1 ➖ 1^1^1^3 1^3 (x ➖ 3x+1).