(129^34+96^38) =[212043 3921703930 3573395047 5179191787 1974830700 5020117631 0367952329 7321308417] mod 11 = 9 - the remainder.
+118724 Heureka, could you please check if what I have done is valid 
I am not sure about the rules for modulus but this is my attempt
What is the remainder when 129^(34)+96^(38) is divided by 11?
129^(34)+96^(38) [mod11]
= (-3)^34+(-3)^38 [mod 11]
=(-3)^34(1+(-3)^4) [mod11]
= 9^17 (1+81) [mod11]
= (-2)^17(82) [mod11]
=( -32*32*32*4)(5) [mod11]
= (-1*-1*-1*-1 *4)(5) [mod11]
=20 mod11
=9 mod 11
