### 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

How many of the numbers shown are greater than 10?

### Largest Expression

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

# Powerful Expressions

##### Age 14 to 16 Short Challenge Level:

Put these expressions in order from smallest to largest:

a) $2^7+2$
b) $2\left(4^3\right)-2$
c) $8^2+4^3$
d) $8\times4\times2$

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