Make a list of distinct positive integers that are obtained by assigning a different decimal digit from 1 to 9 to each of the capital letters in bold in this expression.
(A^{B})/C + (D^{E})/F + (G^{H})/I
How many of these integers are palindromes? How many are tautonymic numbers?
Note:
A tautonymic number is one which can be divided into two equal non-palindromic halves, with each part having at least two different digits. For example, each of 3636, 5252, 6767, 276276 and 56635663 is a tautonymic number - but, none of 4444 and 555555 is a tautonymic number.