Write the numerical coefficient as the cube of 6:



1. Divide each exponent of each base in the radicand, by the index of the root,
2. Find the quotient and the remainder in each case.
3. Write the base to the quotient power in front of the radical.
4. Write the base to the remainder power inside the radical. 



We begin with 63. The base is 6 and the exponent is 3. The index
of the root is 3.  We divide the exponent 3 by the index 3 and get quotient 1
with remainder 0.  So we write 61 in front of the radical, and the
base 6 to the remainder power, 60 inside the radical:



Next we have x14. The base is x and the exponent is 14. The index
of the root is 3.  We divide the exponent 14 by the index 3 and get quotient 4
with remainder 2.  So we write x4 in front of the radical, and the
base x to the remainder power, x2 inside the radical: 



Then we have y18. The base is y and the exponent is 18. The index
of the root is 3.  We divide the exponent 18 by the index 3 and get quotient 6
with remainder 0.  So we write y6 in front of the radical, and the
base y to the remainder power, y0 inside the radical: 



Now since anything to the 0 power is 1*, we can eliminate writing the 0 powers,
and also the 1 exponent in the front.  So the final answer is:



*except 00 which is undefined, which we did not run into.
Edwin