Mike Speciner <ms@alum.mit.edu> wrote:

Some of the cubes and fifth powers are also squares. And some of the cubes and fifth powers are the same, as they are fifteenth powers.

In the text you quoted in that very message, Allan Wechsler said:

...

... but there is some ambiguity here, exemplified by 16 = 4^2 = 2^4. Let us, for the moment, resolve the ambiguity by preferring, for this purpose, the representation with the smallest exponent.