Do your best to plan ahead and provide clear messages about how you will handle power outages and related disruptions. Let students know how you plan to communicate with them in the event of a disruption, with a method that is as robust to power outages and disruptions as possible, keeping in mind that there may be inevitable delays in sending and receiving these communications. Let students know how you expect them to handle assignments, exams, and access to course materials in the event of a disruption. Include these plans in your syllabus. Announce them verbally on Day 1. Be sure all GSIs are aware of these plans. In the week leading up to any exam, both you and your GSIs should reiterate your plans in written announcements to the students.
If you must cancel synchronous lectures because you, your GSIs, or some or all of your students are without power, you may cancel the class, or reschedule it, or provide asynchronous materials (e.g. readings, pre-recorded lectures) once power has been restored.
If you must reschedule an exam, try not to be in an urgent rush to complete the exam. If possible, wait at least 24-48 hours after the return of power, especially for extended outages. It is likely that you and your students will have practical concerns that may take precedence immediately after power is restored.
For more info, the Instructional Resilience Checklist contains a full list of suggestions of what to do before and after a disruption.