Number Theory Problem: 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.

Question

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, even 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 are if they do. Perfect 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? Examples for each d not equal 2 as follows: For d = 0 -> 2^3 = 8; for d = 1 -> 3^2 = 9; for d = 3 -> 67^2 = 4489; for d = 4 -> 33^2 = 1089; for d = 5 -> 2^4 = 4^2 = 16; for d = 6 -> 7^2 = 49; for d = 7 -> 44^2 = 1936; for d = 8 -> 34^2 = 1156; and for d = 9 -> 38^2 = 1444.