Actually this seemingly elementary question had very much surprised me, I though it is quite easy to find such triples described in question, but strangely after trying so many times, couldn't find any, but the hope is there in relatively large solutions, or may be a notable work is there about this issue where I don't encounter yet.

A powerful number by definition is an integer which has all exponents in its prime factors greater than one.

The reference of this question was originally in Quora.

anytwo numbers to be powerful, or only the 'first' two ($x^m$ and $y^n$, in the notation of the Quora question)? $\endgroup$ – LSpice Jun 12 '16 at 22:11