Simplfiying a rational, cube root expression

How would you simplify this? ³√(x^9 / 3y)

³√(x^9 / 3y)

³√x^9
---------- {took cube root of numerator over cube root of denominator}
³√3y

x³
-------- {evaluated cube root of x^9 to be x³ on top}
³√3y

x³ ³√9y²
----------------- {multiplied top and bottom by ³√9y², to eliminate radical in denominator}
³√3y ³√9y²

x³ ³√9y²
---------------- {multiplied in denominator}
³√27y³

x³ ³√9y²
-------------- {evaluated cube root of 27y³ in denominator}
3y

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