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I'm trying to prove

If $m^n=a^pb^q$ for positive integers $m,n,a$ and $b$ and different primes $p$ and $q$ (with $p+q \neq n$), then each of $a$, $b$ and $m$ must be a power of some integer $x$.

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    $6^2=2^2\times3^2$. – 2017-01-02
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    For different primes $p$ and $q$? – 2017-01-02
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    @Servaes Thanks! – 2017-01-02
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    @Servaes You have $m=a=b=2$, and so $a=b=m^1$. So your equation isn't a counterexample. – 2017-01-02

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$4^7=8^3\cdot2^5$ is a counterexample to your claim in which $p$ and $q$ are distinct.

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    Thanks. Changed the question. Please, take a look. – 2017-01-02