Task# Seven to the What?!?

Illustrative MathematicsVaries

At first glance, this might seem like an impossible problem because the number is much too large to evaluate even with a calculator. It requires a starting point, and, to many, such a starting point might not be obvious. Students who successfully answer this problem must 'look for and express regularity in repeated reasoning', and so the purpose of this task is to give students an opportunity to engage in MP8 and to practice working with positive integer exponents. There are two key steps involved in the solving this problem: Recognizing (or at least presuming) that the last two digits of can be found without calculating the number.