The  is cumbersome, so let's substitute  



Write 64 as ,
Write 36 as 
Write 512 as 
Write 200 as 





Divide the first equation through by 
Divide the second equation through hy 

, 

Subtracting exponents of like bases:



Take out common factors in exponents on the right:



Write powers of 2 as 2nd and 3rd powers of 



To make the right sides equal raise both sides of the first
equation to the 3rd power and raise both sides of the second
equation to the second power:








Divide equals by equals.  Since the right sides are equal, the
right side will be just 1.



The left side can be written as



The only exponent of a base (other than 1) that equals 1 is 0,
therefore





Substituting in







Equating the exponents of 2









Solution: (x,y) = (3,2) 

Edwin