The numbers from 1 to 150, inclusive, are placed in a bag and a number is randomly selected from the bag. What is the probability it is not a perfect power (integers that can be expressed as $x^{y}$ where $x$ is an integer and $y$ is an integer greater than 1. For example, $2^{4}

139/150

Step-by-step explanation:

Let's make a list of the perfect squares.

1 4 9 16 25 36 49 64 81 100 121 144

The probability that one of these is drawn is 12/150 = 4/50 = 2/25

Take out 1. So that means there are 11 perfect squares.

11/150 are your chances of getting a perfect square.

1 - 11/150 = 139/150 that you will not get a perfect square.

I would have included 1 in the perfect squares, but the question says not to so you can't.

If the question did not mean that 1 should be excluded, then the answer is 23/25