How do you simplify 8^-2/3?

(2^3) (-2/3) = 2^ (3*-2/3) = 2^ (-2) = 1/2^2 = 1/4 = 0.25

Because the exponent is negative take the reciprocal - it becomes 1 / (8^2/3). then take the cube root of the denominator and it becomes 1 / ³√8². 8²=64, and the cube root of 64 is 4. it is now 1/4, which is as simplified as it gets.