The more interesting it is, because powers exist with all the other individual decimal digits d missing from the otherwise also not decimal digit sharing k, m, and k^m.
So, d = 2 seems to be elusive, or, is indeed the exception?
Easily found examples for each d not equal 2 as follows:
For d = 0...
Find a perfect power k^m > 1 where k, m, k^m do not contain 2 in their decimal digits, nor do share any decimal digit, no matter if k^m might possibly be expressed in more than one way for some value, e.g. 8^2 = 4^3. I do not know if such an integer exists at all, or how many and how large they...