Can a MICRO ATX mainboard be connected with a ATX2.3 Power Supplier(PSU)?

According to the board's manual on gigabyte's web site, it runs off of a standard 24-pin ATX power cable. uming your power supply has a 4-pin (or 6-pin) CPU supplementary power cable (your PSU has both) you should be able to run that motherboard off of that PSU.