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# Power up to 1000

**Answer**: $6$

**Index laws**

$\begin{align}1000&=10^3\\

&=\left(2\times5\right)^3\\

&=2^3\times5^3\end{align}$

So $x=3$ and $y=3$, so $x+y=6$.

**Calculating directly**

$\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 $x+y=6$.

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Age 14 to 16

ShortChallenge Level

- Problem
- Solutions

$\begin{align}1000&=10^3\\

&=\left(2\times5\right)^3\\

&=2^3\times5^3\end{align}$

So $x=3$ and $y=3$, so $x+y=6$.

$\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.

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