SOLUTION: Simplify the expression, and rationalize the denominator if appropriate. Cube root of {{{2x^4y^4/9x}}}

First we cancel the x in the bottom into the x⁴
 in the top getting x³ in the top



Next we break the cube root of a quotient 
into the quotient of two cube roots:



Next we want to get rid of the cube root on
the bottom. It contains 9 = 3*3.  Let's write
9 as 3*3



We can make that 3*3 into the perfect cube 3*3*3 
or 3³ by multiplying it by 3, so we multiply the 
entire fraction by 



Now we multiply numerators and denominators by 
multiplying under radicals:


  


Now the denominator becomes just 3 and we write
the y⁴in the numerator as y³y:



Finally we take the x³y³ out of the radical in 
the numerator and put xy in front:



Edwin