Given that xy=1. Now we have to use this equation to find the value of
[tex] \frac{2^{(x+y)^2}}{2^{(x-y)^2}} [/tex]
[tex] =2^{\left((x+y)^2-(x-y)^2\right)} [/tex]
[tex] =2^{\left(x^2+y^2+2xy-(x^2+y^2-2xy)\right)}[/tex]
[tex] =2^{\left(x^2+y^2+2xy-x^2-y^2+2xy\right)} [/tex]
[tex] =2^{\left(2xy+2xy\right)}[/tex]
[tex] =2^{\left(4xy\right)}[/tex]
[tex] =2^{\left(4xy\right)}[/tex]
Now plug the given value of xy=1
[tex] =2^{4*1}[/tex]
[tex] =2^{4}[/tex]
[tex] =16[/tex]
Hence final answer is 16.
