Track / Stage 2 / 87 of 320 #407 of 2604

When I noticed that $2^4 = 4^2$, I tried to find other pairs of numbers with this property. Trying 2 and 16, I realised that $2^{16}$ is larger than $16^2$. How many times larger is $2^{16}$?

This one wants a proof. Work it on paper, then check yourself against the publisher's own solution, linked below. Be honest about it: the record is only any use to you if it is.

I solved it I didn't Skip

Next problem →

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.