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If $a$ is an integer and $b$ is a fourth power of an integer such that $ab$ is the fourth power of an integer, explain why $a$ is also a fourth power of an integer.

Show that $a$ is the fourth power of an integer if: $b^4$ $(ab)^4$

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HINT: What can you say about the exponents in the prime decomposition of a fourth power?

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    @Dmitri: There you go. An integer is$a$fourth power if and only if the exponents in its prime factorization are all multiples of $4$. So if $ab$ and $b$ are both fourth powers, ...2012-12-10