The power family of distributions have densities

$\displaystyle f(x;\alpha,\theta) = \frac{\alpha x^{\alpha -1}}{\theta^{\alpha}}$, $\displaystyle 0 \leq x \leq \theta$. 0 elsewhere.

If $\displaystyle \theta$ is known, show hat $\displaystyle f(x;\alpha)$ is in the exponential family and find a sufficient statistic for $\displaystyle \alpha$.