Question $3[10\%]$

Consider an economy with a homogeneous good $(x_0)$ a differentiated good with n varieties $)=(1$dotsn. Suppose the utility function of the representative consumer in this economy is represented by:

$U=[x_0,({\displaystyle \underset{?}{\overset{?}{}}}{x}_i^{}{)}^{(\frac{1}{})}]$

Find $($a$)$ the demand function of the $i^{th}$ variety and $($b$)$ the price aggregate.