Compressing and cooling air in a Coolgardie Safe, then decompressing

I'm a 10th grader so it would help to explain how, in the answer to the link above, $$T_{cool}\left(\frac{V_{final}}{V}\right)\left(\frac{P_{ambient}}{P_{cool}}\right)$$ became... $$T_{cool}\left(\frac{P_{ambient}}{P_{cool}}\right)^{2/7}$$

Where did 2/7 come from?