Question

(1/4)^x+y = 256

what are the exact values of x and y?

Answer 1

I assume you meant:
(1/4)^(x+y) = 256
well, 256 = 4^4 , so (1/4)^-4 = 256

your equation becomes:
(1/4)^(x+y) = (1/4)^-4

so x + y = -4

so exact values of x and y are those values whose sum is -4
Lots of them!

e.g. x = 2, y = -6
x = 4567 and y = -4571
etc