Question

4^(x-x^2)=1/8

Answer 1

right side: rewrite 1/8 as 1/(2^3) which is equal to 2^(-3)
new equation

left side 4 = 2^2 or 4^(x-x^2) = 2^2(x-x^2)= 2^(2*(x-x^2)=2^(2x-2x^2)
sorry so long
2^(2x-2x^2) = 2^(-3) almost there
now both sides have a base of 2 do drop it off
2x-2x^2=-3
either factor or use the quadratic formula