Ways to calculate remainder when 47 to the power 95 is divided by 99

99 can be written as 11*9
You can find the remainder of 47^95 with 11 and 9 separately and then use Chinese remainder theorum.
47^95 mod 9 = 2^95 mod 9 = (32*64^15) mod 9 = 5
Similarly 47^95 mod 11 = 3^95 mod 11 = 243^19 mod 11 = 1
So required remainder is of the form 9K+5 = 11K+1. Hence the required remainder is 23.