1) 'A' and 'B' are positive zeroless 2-digit integers which have one digit in common.
A 6-digit sequence, S, composed of only 3 unique digits, occurs in both A^B and B^A.
Find A, B, and S.

2) 'C' and 'D' are two other positive zeroless 2-digit integers which also have one digit in common.
A 6-digit sequence, T, composed of 6 unique digits, occurs in both C^D and D^C.
Find C, D, and T.

Neither S nor T has any leading zero.