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## 'Em'power'ed' printed from http://nrich.maths.org/

If $p$ and $q$ are primes and $p^rq^s= p^tq^u$what can you say about the powers?

If $p^{r/s}$ is an integer what can you say about $r$ and $s$?

All three terms must be the same powers of 2 and 3.