You can put this solution on YOUR website! It is not an equation. Do you see an equal sign?
Set it to zero to make an equation.
256x^4-625y^4=0
It can be factored into three parts
(4x-5y) (4x+5y) (16x^2+25y^2)=0
set each one to zero and solve.
x=0 and y=0 is the solution to (16x^2+25y^2)=0