I can't tell whether you mean:

 or 

I'll assume it's the first way:

Divide 72, and 27 both by 9:





Subtract the exponents of x, 15-8 = 7
Subtract the exponents of y, 15-7 = 8



Rationalize the denominator by multiplyin under the radical by 
to make a perfect cube on the bottom:



 

Take cube roots of numerator and denominator:



Take the cube root of 8 out in front of the radical 
on top as a 2:
Take the cube root of 3³on the bottom which is just 3



Write 3² as 9 since the exponent 2 is less than the index of
the cube root which is 3.
Write the exponent 7 in terms of the largest multiple of the 
root index 3 which does not exceed it. 7=6+1
Write the exponent 8 in terms of the largest multiple of the 
root index 3 which does not exceed it. 8=6+2 
 
 

Write x6+1 as x6x1
Write y6+2 as y6y2



Take x6 out in front as x2 by dividing
the exponent 6 by the index of the root, 3, getting  x2 

Take y6 out in front as y2 by dividing
the exponent 6 by the index of the root, 3, getting  y2

Drop the 1 exponent of the x



You can leave it like that, or you can take the 2 on top and the
3 on the bottom and make a fraction  and write it like this:

x²y²∛9xy²

Edwin

I can't tell whether you mean:

 or 

I'll assume it's the second way:

Divide 72, and 27 both by 9:



Write 72 as 8*9



Take the cube root of 8 out front as 2
Divide the exponents 15 by the root index 3,
and take them out front:



Subtract exponents of x and y and since the larger
exponents are on the bottom, put the result on the bottom:



Edwin