$$\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.