Solve for the digits in this Unique set of Palindrome- Pan Digital Expressions:
$2222$ = $(A/B)^C$ + $(D/E)^F$ + $(G/H)^I$
$2222$ = $(A/B)^I$ + $(D/E)^F$ + $(G/H)^C$
Where, A,B,C,D,E,F,G,H,I are distinct digits representing digits 1 to 9.
The solutions are
Explanation (not full and without a proof of uniqueness)
First, find a power of a single-digit integer (with single-digit exponent) slightly less than 2222. Of course, we have $3^7=2187$. The remainder - $2222-2187=35$ can be represented as the sum of 2 powers - $35=2^5+3^1$ in the easiest way. So, we have $2222=3^7+2^5+3^1$. This is a "good" representation of $2222$, since it contains 2 powers of 3, so we can probably find both solutions, and the power bases are small enough (2 and 3) to be represented as the quotient of 2 digits in several ways. Now, arranging the remaining digits to get the desired quotients is trivial task.