Statement-I:-  $\left|\begin{array}{ccc}x& x& x\\ \alpha & \alpha & \alpha \\ p^3& p^5& p^7\end{array}\right|=0$
Statement-II:- In a determinant if any two rows or columns are proportional then its value is equal to zero
 

In any determinant, if two rows are identical or one is proportional to the other, then the value of the determinant is equal to zero. 

Hence, the determinant $\left|\begin{array}{ccc}x& x& x\\ \alpha & \alpha & \alpha \\ p^3& p^5& p^7\end{array}\right|$ is zero.