A book asks me to prove a statement but I think it is false The problem below is from Cupillari's Nuts and Bolts of Proofs.

Prove the following statement:
Let $a$ and $b$ be two relatively prime numbers. If there exists an
  $m$ such that $(a/b)^m$ is an integer, then $b=1$.

My question is: Is the statement true?
I believe the statement is false because there exists an $m$ such that $(a/b)^m$ is an integer, and yet $b$ does not have to be $1$. For example, let $m=0$. In this case, $(a/b)^0=1$ is an integer as long as $b \neq 0$.
So I think the statement is false, but I am confused because the solution at the back of the book provides a proof that the statement is true.

Your counterexample is valid. But the statement is true if $m$ is required to be a positive natural number or positive integer.
Alternatively, note it's not if true $m$ is required to be negative.
In my opinion, it seems like you were supposed to assume $m>0$.
