GTX 1070 with 500W PSU

The problem here is not the amount of watts, but the quality of the PSU. And sincerely, that PSU seems to be really BAD quality.
You REALLY want to avoid that PSU. You can get a lot better PSUs for the same price, or sometimes even less.
Have a look here:
http://www.tomshardware.co.uk/forum/id-2547993/psu-tier-list.html

With a GOOD quality unit, 500W is enough for one 1070. Evga, seasonic, xfx, superflower and a lot more are good.
 
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