a & gt-( 1+2^x)/4^x

=-( 1/4^x + 1/2^x)=-( 1/2^(2x)+ 1/2^x)=-(b+b^2)(b= 1/2^x， 1/2 & lt； = b< is infinite)

Obviously, when the symmetry axis of y =-b 2-b is x=- 1/2, then 1/2.

So b=- 1/2 gets the maximum value -( 1/2+ 1/4)=-3/4.

So a & gt-3/4