There are four different Power Armor types: T-45, T-51, T-60, X-01. The video below shows how to easily find some of them early in the game. The type of armor you get depends on your character level. If you are only Level 5, chances are you will get T-45 parts, which are the weakest. If you are Level 50, you probably will get T-60 and X-01 armor. However, it is slightly random what armor type you will find in each area. Save the game before collecting parts. If you do not like the part you get, load the saved game to see if you get a different part next time. Most of the parts already have fusion cores installed. Thus, if you simply want a fusion core, you can check these locations and extract it from the Power Armor.
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