For our introduction to exponents, here are some of the pages we worked on, with some student samples. I got this idea from talking to another teacher over summer that said she always did one day just talking about squares, rather than exponents. She said she had students draw squares with different areas, and talk about their dimensions. I turned it into an exponent tower, but I'm sure it's been done before somewhere. 
Once we were done with squares, we started talking about other exponents. I found this free worksheet, and I loved how it broke it down for them. (As a side note, yes, I teach high school. And YES, this is a middle school topic. But, YES, they are this far behind, and need this basic of a review.)
We explored patterns...
And then practiced over and over and over.
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