Help. ​

√ [ 3 x^12 y^10 ]

_____________

√ [5 x^6  y ^3 ]

We  are using the property that   a^m / a^n   =  a^(m - n)

√ [ 3 x^(12 - 6)  y ^ (10 - 3) ]

_______________________

√ 5

√ [ 3 x^6  y^7]

___________

√5

Now...to determine how many powers to take out and how many to leave in :

Take   6 / 2   =  3 powers of x come out

And  7/2  =   3 + 1/2       =    3 powers of y come out  and 1 stays in

So we have

x^3 y^3 √ [ 3y ]

____________                  rationalize the denominator by multiplying op/bottom by √5

         √5

x^3 y^3 √ [ 3y ] √5

_______________

     √ 5 √ 5

x^3 y^3  √ [ 15 y ]

_______________          the second answer is correct   

           5