Let $a$ and $b$ be two elements in a commutative ring $R$ and $(a, b) = R$, show that $(a^m, b^n) = R$ for any positive integers $m$ and $n$. I stumbled across a question that I have no idea how to start.
I know the questions asking to show that the multiples of $a$ and $b$ as an ordered pair make still make the whole ring. 
Any sort of hints or suggestions to start? I don't really want an complete solution, just some sort of hint to start the question.
Thank you!

Write $1$ as a linear combination of $a$ and $b$.  Then raise both sides to the $m+n$ power.
