Question

3sqrt 512x^14/y^3

Answer 1

\[\sqrt{?} =3*16 x^{7}\sqrt{2} /y \sqrt{y} =48\sqrt{2} x^{7}/y \sqrt{y}\]

Answer 2

It is good to learn your cubes, so these problems get easier. I have my classes learn these. Most developmental algebra books only go this far.
2^3=8
3^3=27
4^3=64
5^3=125
6^3=216
7^3=343
8^3=512

I am attaching a file to show this worked out.
When taking roots of variables, divide the variable exponent by the root (14/3=4 and 2/3). This means that x^4 will come outside of the radical and the remainder x^2 will remain inside the radical. In the case of the y^3, 3/3 is 1 with no remainder, so no 'y' will be left under the radical.

Let me know if this helps.