Problem solving with exponents

This post by Michael Pershan has an excellent way to give students opportunities to play around with exponents and problem solve with them.

The basic idea is, give students a bunch of dots in an array, and ask them to find ways to change the picture so that it represents a power.

A related, and more generic, question is:

How do I change this diagram/image/equation/formula so that it represents <something else>?