What is Rational About an Exponent?

I have been helping a friend paint his house this week so I have not been able to write as much content for my new website as I had hoped. However, I was able to work on an article about a method of introducing rational exponents. It is not complete, nor completely edited (my editor a.k.a my wife, has been working insane hours this week) but it will give you an idea about the content I hope to create. Let me know what you think.