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?

Power up to 1000

Age 14 to 16 Short Challenge Level:

\begin{align}1000&=10^3\\ &=\left(2\times5\right)^3\\ &=2^3\times5^3\end{align} So $x=3$ and $y=3$, so $x+y=6$.

If you don't want to use index laws, but want to calculate directly, you can use the method shown below. This also shows why the index laws work!
\begin{align}1000&=10^3\\ &=10\times10\times10\\ &=\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\\ &=2\times2\times2\times5\times5\times5\\ &=2^3\times5^3\end{align} So $x=3$ and $y=3$, so $x+y=6$.
You can find more short problems, arranged by curriculum topic, in our short problems collection.