9^11 = 9 (mod 100), so we need to find 8^...^1 (mod 10). 8^5 = 8 (mod 10), so we need to find 7^...^1 (mod 4). 7^3 = 7 (mod 4), so we need to find 6^...^1 (mod 2), but this is clearly 0, so 7^...^1 = 1 (mod 4) ==> 8^...^1 = 8 (mod 10) ==> 9^...^1 = 9^8 (mod 100) = 21 (mod 100).