Substitute each of the letters by a different digit from 0 to 9 to satisfy this system of alphametic equations. None of the numbers as well as none of the exponents contains a leading zero.

- (
**DID**)^{W} = **F**^{XA}, and:
- (
**FLY**)^{A} = **Y**^{LI}, and:
- (
**LOW**)^{O} = **I**^{LT}

I understand "FLY" would be (100*F)+(10*L)+Y, but how are the multiletter exponents to be read?

Does XA mean (X * A) or ((10*X) + A)? Please clarify unless this ambiguity is part of the puzzle (e.g. only one interpretation would have a solution).

This depends upon the conventions in use for alphametics, which are not standardized. (In any case, rather large exponents! -- perhaps best left to those with Mathematica.)