The power of God [dunamis gar theou] in 1.16 is evidenced in the righteousness of God [dikaiosune gar theou] in 1.17. This righteousness is one that is credited to the account of everyone who is believing in the perfect life and wrath-absorbing death of Jesus on the cross [3.21-26]. This righteousness shows the power of God because Jews and Gentiles are all sinful and accountable before a holy God [1.18-3.20]. Their impotence to righteousness means that they are powerless on their own. They need another, alien righteousness to be declared "not guilty" in the courtroom of the Just and the Justifier [3.26].
This reality of justification by faith is unfurled in the believer's life by living according to the Spirit. Paul shows the universality of sin [chs 1-3], the right-standing before God that is available [ch 4], the hope that a right-standing entails [ch 5], the problem of sin [ch 6], and the problem of the law [ch 7]. He does not discuss how to live in these truths until ch 8. In chs 1-7, he uses the word "spirit" [pneuma] 5 times. In ch 8, he uses the same word 22 times! "Walk by the Spirit, and you will not carry out the desires of the flesh" [Gal 5.16].