Why does taking a gamma value > 1 make the image darker?

If I've understood gamma correction correctly (and I probably haven't), a gamma transform to an image raises the value of the intensity level of the input pixel to the power of gamma, where gamma can be greater than one or less than one.

Pout = (some_constant) x Pin^(gamma)

In every example that I've seen, a gamma value < 1 makes the image lighter (raises intensity of lower intensity pixels) and a gamma value > 1 makes the image darker. This seems counter intuitive to me since a gamma value > 1 should increase the intensity levels of all the pixels making it lighter and more saturated.

Can someone explain this to me? Where am I going wrong?

Summing it up [0; 1]$^\gamma$ is going counter-intuitive.