Indices and surds

$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

Find the sum of this series of surds.

When you stack powers, how do you evaluate them?

Is this surd sum exactly 3?

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?