An integer is randomly chosen from the integers 1 through 100, inclusive. What is the probability that the chosen integer is a perfect square or a perfect cube, but not both? Express your answer as a common fraction.

Answer 1

squares ... 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100

cubes ... 1 , 8 , 27 , 64