How do you tell it to simplify and get fractional exponents?

[clickykeys]

I'm taking calculus 3 and we're playing with partial derivatives. I'd like the Prime to give me answers in a format that ends up in fractional exponents.

For example:

\[f(x,y)=\sqrt{x^2+y^2}\]
\[f_x=\frac{x}{\sqrt{x^2+y^2}}\]
\[f_{xx}=\frac{y^2}{(x^2+y^2)^{\frac{3}{2}}}\]

The Prime gives me:

\[f_{xx}=\frac{y^{2}}{(x^{2} \sqrt{x^{2}+y^{2}}+y^{2} \sqrt{x^{2}+y^{2}})}\]
If I hit that with a simplify() then a collect(), I end up with this:
\[f_{xx}=\frac{y^{2}}{\sqrt{x^{2}+y^{2}} (x^{2}+y^{2})}\]

Are there any CAS commands that I can use to convert that into the version with a 3/2 exponent in the denominator? I think it would be easier to use that form keep going into higher order derivatives. Thanks!