Some people might find this stupid, but at first i had no idea how to use this perk, at level 3 it says that you can eject your core and cause a explosion, at first i had no idea how to do this, but after some time i finally figured it, heres what you do.

Step 1: make sure you have no grenades selected.
Step 2: make sure you're inside some power armour with a core.
Step 3: press your grenade hotkey ( the key that you throw grenades with).
Step 4: make sure your back is facing your target.

Congratulations! now you'r a certified nuclear physicist :)