Product of a geometric series from it's middle term If the $5$-th term of the G.P is its middle term and its value is 2,then find the product of all terms of this GP?

My approach:

Since $a_5$ is the middle term, so the GP contains 9 terms.

$$P_9 = a\cdot ar\cdot ar^2 \cdot ar^3 \cdot 2\cdot ar^5 \cdots ar^8$$

which leaves us $P_9 = 2\cdot (ar^4)^8$ ... I am not getting how to proceed further? Is this approach even correct?
The fourth term is $2/r$ and the sixth term is $2r$.  What happens when you multiply these?  What about the third and seventh terms?
The fifth term is the middle term which means there are $4$ terms to the either side of the middle term (a total of $9$ terms). Thus the product of the terms of the GP is $2^9=512$.