Answer:
[tex]75 {x}^{ \frac{3}{2} } {y}^{6} {z}^{ \frac{11}{2} } [/tex]
Step-by-step explanation:
First thing is to multiply. We don't need to bother with the root for now.
[tex] \sqrt{15 {x}^{2} {y}^{11} {z}^{4} } \times \sqrt{5xy {z}^{7} } = \\ \sqrt{75 {x}^{3} {y}^{12} {z}^{11} } [/tex]
All I did was multiply the numbers and added the exponents for the variables.
Now all we have to do is divide the exponents in half for the variables, nothing is needed additionally for the 75.
[tex]75 {x}^{ \frac{3}{2} } {y}^{6} {z}^{ \frac{11}{2} }[/tex]
There you go, just a few steps and you have your answer.
You can simplify further by moving the answer for the root infront of the square root so it isn't as sloppy. This would make the simplest for to be
5xyz^5 (3xy)^(1/2)
