Proving $\{9^n|n\in \mathbb Q\} = \{3^n|n\in \mathbb Q\}$ The statement is: $\{9^n|n\in \mathbb Q\} = \{3^n|n\in \mathbb Q\}$. 
I am more familiar with traditional proofs. Do I just split up $9^n$ into $3^{n}\times 3^{n}$?

Observe that for any $\;n\in\Bbb Q\;$
$$\begin{cases}9^n=3^{2n}\\{}\\3^{n}=9^{n/2}\end{cases}\;\;\;\implies\left\{\,9^n\;:\;n\in\Bbb Q\right\}=\left\{\,3^n\;:\;n\in\Bbb Q\right\}$$
