How to evaluate the determinant of this matrix?

Question

Let $x_1, x_2, ... , x_n$ be real numbers, and $A=(a_{ij})$ be the n by n matrix whose entries are $a_{ij}=(x_i)^j$. Evaluate the determinant of A.

Answer 1

It is something like Vandermonde matrix. It seem to me that the value of it if neither of the entries is 0, should be equal $\prod_{k=1}^{n}x_{k}\prod_{1\leq i<j\leq n}(x_{j}-x_{i})$.