Working with Fractional Powers

Not sure how to solve the last part of this problem. The original equation reads:

$\displaystyle \sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7}) $

So then you raise the powers to get some nicer exponents to work which looks like this

$\displaystyle x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1} {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7} {2})$

and here is where I am lost, the author adds the exponents of the variables and ends up with

$\displaystyle x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}$

How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!