Is it possible to have three line segments, $a$, $b$ and $c$, in an arrangement such that the geometry implicitly shows that the length of $c$ is equal to the length of $a$, raised to a power, which is the length of $b$? i.e. $c=a^b$
I'm looking for something similar to how you can show three segments, where $c=a \times b$ like this. I don't, however, want to use this to multiply $a$ by itself $b$ times. I have seen similar questions being answered this way, but it won't help in my case. I want the variable $b$ to be able to change without adding or removing geometry.
The geometry doesn't have to be constructable using just straightedge and compass.