I'm a little confused as to the solution of a radical expression. My goal is to simplify it as much as I can. Here is the expression:

\(\displaystyle

\sqrt{\frac{9x^7}{16y^8}}

\)

The solution which I thought would be right is:

\(\displaystyle

\frac{3x^6\sqrt{x}}{4y^7\sqrt{y}}

\)

Using Mathway.com, however, it's telling me that the answer is:

\(\displaystyle

\frac{3x^2\sqrt{x}}{4y^4}

\)

I would greatly appreciate if someone could explain how I got the wrong answer so I may learn from my mistakes. :] Thank you all very much.

Colton