NEGATIVE EXPONENTS

One of the most bothersome concepts in Algebra or Pre–Algebra in some 

places is the negative exponent.  We know that the sign of the exponent

has nothing to do with the sign of the number, but tell that to a learning

Algebra I student.  This is a great place for my preaching of patterns in

Math.  If you have not done this already I suggest you try.

         2^4 = 16   A place to start, use any base

                                           

         2^3 = 8     8 is ½ of 16

                                           

         2^2 = 4     4 is ½ of 8

                                           

          2^1 = 2

                                           

          2^0 = 1

                                           

           2^–1 = ½

           2^–2 = ¼ or 1÷ 2^2

           2^–3 = 1/8 or 1 ÷ 2^3

As we see, having a negative exponent makes things smaller 

but not negative.  Keep patterns in mind when you teach.

Good luck.  

        a^–n = 1/a^n