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 $x+y=6$.