now we have to start looking at more complicated

Question

Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form

                                                                    b ^m/n

where m and n both are integers.

We will begin simple by looking at the given special case,

                                                         b^{1/ n}

where n refer to an integer. Once we have figured out the more general case provided above will in fact be pretty simple to deal with.

Let's first described just what we mean by exponents of this form.

        a= b ^1/n           is equivalent to                        aⁿ  =b

In other terms, when evaluating b ^1/n, we are actually asking what number (in this case a) did we rise to the n to get b.  Frequently b ^1/n is called the n^th root of b.