When reducing integers in a radical, you must reduce based on the index, which could be squaring or cubing the number.

For example:  ³√27x³  (Cube root of 27 x cubed)

To pull the  27 out from under the cube root sign, you would cube the number 27 and put a 3 in front of the radical.

 

For example ³√27x³ (Cube root of 27 x cubed)

To pull the x³ out of this radical and put it in front of the radical, you would divide x³ by the index (3) and put the x out front.

 

 

The difference between reducing integers and exponents is that when you reduce exponents, you divide by the index, and when you reduce integers, you root by the index.