# Raising to power geometrically

On a straight line with marked origin 0 and unit 1, two points x and y are given. Is it possible, by any finite method, to geometrically define x^y if the given y is not a rational but an arbitrary point?

• So, is the question something like: Given three marks $x$, $y$ and $z$ where someone claims that $x^y=z$, is there a finite geometric construction (possibly involving other guessed points) they can use to prove they are right? – Henning Makholm Jun 1 '16 at 12:59

Answer to an earlier version of the question which asked to construct $x^y$ instead of merely defining it:
No, at least not if "any finite method" means compass and straightedge -- for example this is famously impossible when $x=2$ and $y=1/3$.