the next thing that we must acknowledge is that

Question

The next thing that we must acknowledge is that all of the properties for exponents. This includes the more general rational exponent that we haven't looked at yet.

Now the properties of integer explore are valid for this section also then we can see how to deal with the more general rational exponent. In fact there are two different ways of dealing along with them as we'll see.  Both of the methods involve via property 2 from the previous section.  For reference reason this property is,

                                                                  (aⁿ )^m  = a^nm

Thus, let's see how to deal along with a general rational exponent.  First we will rewrite the exponent as follows.

                                                  b ^{m /n}   = b^{(1/n) (m)}

In other terms we can think of the exponent like a product of two numbers.  We will now use the exponent property illustrated above.  Though, we will be using it in the opposite direction than what we did in the earlier section.  Also, there are two ways to do it.  Here they are following,

b m /n  = ( b ^1/n )          Or                             b ^{m/ n}   =(b^m )^1/n

By using either of these forms now we can evaluate some more complicated expressions