Evaluate each of the following.

 (a) 25^1/2

 (b) 32^1/5

Solution

 (a) 25^1/2

Thus, here is what we are asking in this problem.

                            25^1/2  = ?

By using the equivalence from the definition we can rewrite this as,

                           ? ²  =25

Thus, all that we are actually asking here is what number we squared to get 25.  In this case that is (hopefully) simple to get.  We square 5 to get 25. Thus,

                                                    25^1/2  = 5

 (b) 32^1/5

Thus what we are asking here is what number did we move up to the 5^th power to get 32?

                               32^1/5  = 2               because            2⁵  = 32