Suppose that x and y are positive integers such that x^2y^3=46656. What is the sum of all possible values of x?

 

  x           

216         
27          
8            
1           

- 216

- 27

- 8

- 1

x = 216 + 27 + 8 + 1  - 216 - 27 - 8 - 1= 0 

The only positive integers that balance the equation are:

 

x = 216 + 27 + 8 + 1 = 252