Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Rooted Via 10

Weekly Problem 22 - 2013
How many of the numbers shown are greater than 10?

Largest Expression

Weekly Problem 36 - 2006
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

Power of 3

Age 14 to 16 Short Challenge Level:

What number needs to replace the  as the power of 27, so that
$3^{2016}+9^{1008}+27$ $=3^{2017}$?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.