Help please, thanks

x                y

216           1
27            4
8              9
1              36

 

x = 216 + 27 + 8 + 1 = 252 

 

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

 

factor(46656) = 2^6*3^6

\(2^6*3^6\\~\\ (2^3)^2* (3^2)^3=8^2*9^3\\ (3^3)^2*(2^2)^3 =27^2*4^3 \\1^2*(6^2)^3=1^2*36^3 \\(6^3)^2*1^3=216^2*1^3\)

 

 

Just as guest already determined.