Unless a Power explicitly says otherwise:

It only affects one single target land. “Destroy up to 3 Explorers” will let you Destroy up to 3 Explorers in the same land — not in multiple different lands. If a Power has multiple effects, they ALL apply to the same land.

It only affects the current turn. “Dahan have +3 Health” or “Invaders do not Ravage in target land” affect this turn only, not the rest of the game. Any permanent changes to the game will be represented by changes to a board: pieces leaving, Fear Markers moving, etc.

It can only be used once this turn. You cannot choose to pay for a Power Card twice and use it twice. Innate Powers only trigger once even if you have twice as many Elements as you need. If something makes a Slow Power Fast, you only get to use it during the Fast Phase, not both Phases.