Which of the following is equal to sqrt 50a^6b^7

Your question implies there are choices given with possible answers. As I do not have those in front of me, I will show you how to simplify the radical. It is likely that the answer you seek is the simplified radical.

To simplify we use the following identity: for positive values of a and b,

That identity allows us to re-write what we are given as . Let us now consider each of these separately.

Though 50 is not a perfect square it can be written as 25 x 2 and 25 is a perfect square. Thus, we obtain

Next we consider which is a perfect square as it is equal to . Thus,

Lastly, we consider which can be written as and since is a perfect square we obtain the following:

Putting that all together we obtain