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 $3^{n}\times 3^{n}$?

Hint: Suppose $x \in \{9^n\:|\:n \in \mathbb{Q}\}$. Then there exists $a \in \mathbb{Q}$ s.t. $x = 9^a$. So, $x = 9^a = 3^{2a}$ and $3^{2a} \in \{3^n\:|\:n \in \mathbb{Q}\}$. Hence, $\{9^n\:|\:n \in \mathbb{Q}\} \subseteq\{3^n\:|\:n \in \mathbb{Q}\}$. Try to show the opposite inclusion.
