Raise signal to power?

Is there a way to perform distortion by raising a signal to a power?

More specifically: x => sgn(x)*(abs(x))^(alpha)
where sgn(x) = 1 if x > 0, 0 if x = 0, and -1 if x < 0.

Perhaps this could be added to the built-in distortion effect?

Yes. You can do that in the Nyquist Prompt. For example, raising the signal to the power 4:

;version 4
(mult *track* *track* *track* *track*)