45⁵⁰ is a huge number so subtracting 9 from it is pointless since the number is well out of range for a calculator. But an estimate can be given for the whole expression: it’s approximately 1 followed by 81 zeroes!
But it is possible to find the remainder which is always 36.
45-9=36 so when we divide by 44 the remainder is 36.
Now take 45⁵-9=184528116 and divide by 44=x+36/44, where x is an integer.
In fact all powers of 45 when divided by 44 have a remainder of 1. This is because 45=44+1. 45ⁿ=(44+1)ⁿ.
If we expand the binomial we get a series of terms which, apart from the last term, contain some multiple of 44. The last term is 1 no matter what n is. So when we divide by 44, we are always left with 1.
We can write the original expression as 45⁵⁰/44 - (44-35)/44. So we have in terms of remainders 1+35=36.