Remainders of large powers

Students will learn how to find the last digit or last two digits of a whole number raised to a very large whole number power. Start by demonstrating that remainders repeat. This happens because the last digits of a product are only dependant on the last digits of the multiplicands. Here's an example demonstration. Once your students are comfortable with this idea, give them a couple practice problems. Include at least one problem asking for the last digit and at least one problem asking for the last two digits. Asking for more digits would be tedious, so I advise against it. Next, give your students this challenge. Finally, give them this one.