Can the gigabyte a75 motherboard run on 400w power supply

I'm not sure what you mean. The motherboard doesn't determine how much power you use, it's what you have plugged into it.

Occasionally, you'll have a power supply that doesn't have the right connectors for a motherboard (24-pin vs. 20-pin, or the 4-pin auxiliary), but most of them these days are designed to accommodate both.