Question

Please explain this to me!

Answer 1

Next time, please be sure to include all of the instructions.

This is an unusual problem in that the indices of the roots are different (2 and 4).

It might be a bit easier to rewrite this problem using fractional exponents:

      1/2
 10
------------
     1/4
  8

Here I'd strongly suggest elilminating the root in the denominator.  You could do this by mult. both numerator and den. by 8^(3/4):

        2/4    3/4               2     3    1/4            2/4     3/4
    10       8               (10  * 8    )              10      * 8
--------------------- = ----------------------- = --------------------  
     1/4     3/4                                                   
  8        8                            8                             8

                                          2/4                      3/4               3/4       9/4
Can't do much with the 10      .  However, 8       =  (2^3)        = 2

and so you wind up with                       
                                               9/4
                                             2
                                            --------
                                                 8

which cannot be simplified further (especially if we don't want a radical in the denominator).