Indices and Surds

Climbing Powers

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

$2\wedge 3\wedge 4$ 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 $\sqrt{2}$?

The Root of the Problem

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the sum of the series.

Power Stack

Stage: 5 Short Challenge Level: Challenge Level:1

When you stack powers, how do you evaluate them?

Quick Sum

Stage: 5 Short Challenge Level: Challenge Level:1

Is this surd sum exactly 3?

Irrational Arithmagons

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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