You may have a problem related to surge when the power came back on. The safest and best thing to do is unplug the appliance and call a professional. But first:
Does the power cord get hot to the touch when plugged in and drawing power? If yes the problem is in the appliance-something happened when the power went down, maybe a surge, or something happened to the appliance when the power came back on, again, maybe a surge. Either way, it's a job for the appliance repairman, especially if it is a newer model appliance with computerized workings. Check your owner manual for the troubleshooting section. Trying to fix it yourself will void the warranty.
Does the outlet get hot when the appliance is plugged in? If yes, you have a problem in the outlet, and this is a job best left to the pros who have the tools and training to track down the source of the problem.
Does the breaker get hot when it trips? If yes, leave the breaker off, and go through the house to eliminate as much load on the whole electrical system as you possibly can while you wait for a professional to arrive and check everything out.
Usually when power is restored after being off for a few days there can be a strong surge, flicker, then surge-anything you didn't turn off and unplug when the power went out has just been jolted and could have a problem.
Next time the power goes out, go around the house and turn everything off then unplug-everything. When power is restored, replug one appliance at a time, then turn the item on as needed.
When people are preparing for an emergency they are rarely reminded to turn off an appliance before unplugging it if the power goes off, but it would save a lot of appliances if people understood that. Even though the appliance is off because there is no power getting to it, the on switch is still on, and when power is restored the appliance will come back on, which can create quite a problem for the electrical system it's all plugged into at your home.
This is especially important with any kind of a home entertainment system (TV, DVD, cable box, etc), especially the ones that are on standby when turned off, and computers, battery chargers, etc.
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