Big Powers


At first glance, a challenging problem; but no algebra is required to justify the solution.

Students who meet this problem for the first time may need a significant amount of support in structuring a solution so it is useful to be able to find similar tasks to which they may apply their new-found understanding.

You can find a number of similar problems on the NRICH site - for example:
Power crazy
What an odd fact(or)

It is important to be able to justify any pattern. How can you be sure it continues?