Tier 1 Powerful Gear sources (+2-3 Power):
Flashpoint
Nightmare Hunts
Defeating 30 Nightmares (Moon vendor)
Luna's Calling (Lectern of Enchantment)
Vanguard Strikes playlist
Nightfall: The Ordeal playlist
Complete eight Bounties for each Tower vendor

Tier 2 Powerful Gear sources (+3-4 Power):
The Sundial (Season of Dawn activity)
Crucible (Core playlist)
Crucible (Rotator playlist)
Weekly Moon Story Mission
Gambit playlists
Earn Clan XP for Tower vendor

Other non-Tier Powerful Gear sources:
Prime Engrams (essentially a permanent Three of Coins buff in-all-but-name)
Exotic Engrams
There are also a handful of 'one-time' sources of Powerful Gear, such as Exotic quest rewards.
Year 3 Raid (Garden of Salvation) encounter wins and completions
Pit of Heresy dungeon
Nightmare Hunts (Master difficulty)
Nightfall: The Ordeal (score 100,000 points or more)
Iron Banner Bounties