There has been outage in my house for the past 8 hours.
I want to know if there's a better way of saying it or if this is grammatically correct.
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If we change "outage in" to "a power outage at", the sentence becomes grammatically correct.
There has been A POWER outage AT my house for the past 8 hours.
That still sounds a bit odd though. Usually a power outage refers to everybody that lost power, not just your house. I think this sounds better:
There has been A POWER outage IN MY NEIGHBORHOOD for the past 8 hours.
I also like boatseller's answer. He gives the more colloquial way to describe a power outage, using the phrase "the power's out".