According to this Reddit post, the various gear soft caps are:
- Blues and merchants to 500
- Daily and weekly challenges (the gold star things in the director) to 520
- Nightfall to 540
- The Dreaming City to 560
- Normal raid to 580
- Prestige raid to 600
Each activity will give you drops that are up to +5 power from your current maximum power until you reach the soft cap. From there, you will get drops that are up to +1 power from your current maximum power.