After the power outage, the power supply was damaged (I hear the small explosion on computer). After I unplug the computer power cord I smell the power supply which it smell burned. Will motherboard go damaged if power supply damaged?
It's hard to tell, there is a chance that some of your other components could have been damaged when your Power Supply Unit died.
The PSU could of potentially destroyed every component in your system, this would be very unlikely though, and your best way to find out is to simply replace the PSU and see if your PC boots up correctly.
My dad lives in an area with lots of lightning storms and he has gone through 2 PSUs. Once it killed the motherboard and once it didn't. Both times his computer was connected to a reputable power strip/power cleaner. I've now connected him to a decent sized APC UPS to try and prevent future problems.
Take warehead0's advice, replace the PSU and cross your fingers it was the only thing that went.