Looking for the correct answer for this problem:

square root of 10x to the sixth power times y cubed

times

the square root of 2x to the fifth power times y

If you are looking for the direct answers to the questions, then you most likely will not find someone here who is willing to do your homework for you. It's really not the policy of this site for people to do other's homework for them. However, would you be interested in someone guiding you in how you might come up with the correct answers yourself based upon a dialogue with someone who might be willing to help you? You will learn much better that way.

You also might like to check out the guidelines that have been given on the following link concerning homework questions.

https://www.askmehelpdesk.com/math-sciences/announcement-font-color-ff0000-u-b-read-first-expectations-homework-help-board-b-u-font.html

Is this what you mean?:

\sqrt{10x^{6}y^{3}}\cdot\sqrt{2x^{5}y}

Combine under one radical sign and then apply the rule a^{m}a^{n}=a^{m+n} and (a^{n})^{m}=a^{mn}

Chances are you won't reply anyway, so there's all I can give.