Most the videos listed below cover the meaning, basics, and rules of exponents. Bottom of page has link to videos on scientific notation and rational exponents--which require a knowledge of radicals.
Here is a funny quote I found (not sure of author): "You can't teach exponents to atheists- - they don't believe in higher powers."
NOTE: See attached handout (bottom of page) titled Laws of Exponents. It covers the laws of exponents which are also covered in the videos below. The handout covers more examples, and has a problem set. The answer key to the problem set is also attached.
Exponents 3-Product Rule for Exponents
Go to this link for videos on Scientific Notation
Go to this link for videos on Rational (Fractional) Exponents