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Would a Fiio K1 provide ample power to these?
Disclaimer: Not super knowledgeable - specifically comparing loudness in dB with what levels I listen to
Quickly looking at Fiio K1 specs, it has a Max 3.25Vpp which is a little below 1Vrms. 1Vrms @ 1khz for K7xx is 105 dB (if I'm guessing specs correctly, everyone seems to fudge units).
Lots of guess work going on, but it might barely be enough for satisfying experience in a quiet room. With my fiio x1 (4Vpp on specsheet but who knows how accurate that is with fully charged batt), k7xx gets loud but Fiio x1 distorts at/near max volume -> you probably wont' get 105dB accurately on the K1- and closer to 101-102 dB or less (which is substantially quieter on dB scale).
With that said, I wouldn't listen to K7xx at max volume on F x1 (107'ish dB? - also assuming 4Vpp correct) even if it were accurate - awfully loud in quiet room. If you like plenty of thumping bass that's a whole new can of worms and wouldn't recommend k7xx with Fiio K1. I could be completely wrong though because disclaimer plus i don't own K1 >.<. Lots of guesswork going on.
TLDR: Ample? not really but might be enough for your needs. Review few ppl down claims 12V supply not enough (probably 9Vpp'ish swing on amp). You won't get the true experience the headphones can offer. On the bright side you won't be at high risk loosing your hearing because of it.
I listen at pretty low volumes, but I just ordered the original Fulla, which should be a bit more powerful.
Power is not the main reason to get an amp. Increase in sound quality is the main purpose of an amp. You can pretty much ignore power output specifications when comparing amps. Price is a good indicator. Unfortunately, you can't really tell the quality of an amp from just reading specifications. Some of the best amps are not that powerful because they run on Class A topology which consumes a lot of electricity.