Greetings, Nightshade:
I’ll give it a go, though I’m sure others who have a better handle on this will chime in and more accurately direct you, as I don't doubt there's more to it than I've been able to surmise--it always seems to be that way
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That being said…
The POW characteristic can influence luck rolls as the formula for the luck roll is POW x 5. It stands to reason that the higher the POW a character has, the better the luck roll...I don't see an expenditure of power points as part of that formula though. If it is, I've overlooked it.
In relation to Fate Points a character can use power points to influence the fate of a character in two ways according to the book. He/she or it, “…can spend five power points to re-roll any percentile dice when the results are unfavorable” but no re-rolling the ''re-roll'' and no xp check for it either.
The second way is an expenditure of, ''…five power points to ignore a skill and trust fate, using your Luck roll as if it were Difficult to determine the chance of success or failure, rather than the relevant skill.'' It’s for skills only—not for a resistance or characteristic roll and no good for gaining xp or POW increases either.
An expenditure of three power points per point of damage allows a character to, ''…ignore [said] damage…from a single attack…''
The ''basic system'' can be expanded at GM desire and discretion in various ways: to shift die rolls more favorably, inflict more damage to an opponent, to add more depth to a character’s past: ''you suddenly remember an old tale your grand-father told you as a child that seems key to unlocking the mystery of…'', etc. etc.
Though the box containing the rule on page 176 of the 0-Edition does not flag it as optional (as other optionals are) the text describes it as such and that it is a new rule not previously featured in any ''previous editions of the Basic Roleplaying system.''
Hope this helps!
Cheers,
Sunwolfe