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Infragisticsnetadvantageultimate2012vol1keygen

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Infragisticsnetadvantageultimate2012vol1keygen.pdfQ:

$(ab)^n$ equals $a^nb^n$ if and only if $a=\pm b$.

This is a question from a past exam paper:

For any $a,b \in \mathbb{Z}$, show that $(ab)^n=a^nb^n$ if and only if $a=\pm b$.

I’m completely stuck on this one and any hints would be much appreciated.

A:

We have that $a=b=\pm 1$ is never a solution. For the other solution, assuming that $a^n=b^n$, we have
$$(ab)^n=(a^n)(b^n)=a^nb^n$$
which implies that $a=\pm b$.

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