Looking for explanation for LOOKUP parameters like 7^7, 8^8, 9^9

You need just to put big enough number that will never be reached.

So if you have numbers in column like: 1,2,4,5,3,6,4,3,5,6,... then 10 is enough...
But if you get number 11 then it wont work.

So you can put 100.
Etc...

If you have dates then 100 won't be enough either.

So instead of think what is biggest number you can get you can put biggest number in excel: 9.99999999999999E+307

If you are lazy, like me, then you can write 99^99 that is quite big: 3,68E+197

I DON'T suggest to use 9^9 since it's "small" number. Only 387420489

espetially not smaller...

1^1 is just 1 and it will always fail (unles you use negative numbers). Even percentage between 0 and 1 can sometimes has 1 and return unexpected result.