Powers are algebraic
expressions which are based
on the
idea of repeated
products of some
symbol with itself.
Example: the third power of x is x^3 = x * x * x.
This idea can be extended to fraction powers,
so that x^(1/2) is equal to that y
such that y^2 = x. Then more subtle trickery can be used to extend the idea of powers to irrational numbers.