Small issue with latex!

Question

I'm a high school student doing a research on LaTeX. I'm learning in the process of doing so, however, I can't find anywhere how to express the following:

Answer 1

$$ \nabla f= \begin{pmatrix} x_1^{n-1} \\ x_2^{n-1} \\ \vdots \\ x_n^{n-1} \\ \end{pmatrix} $$

Here is the syntax used:

$$
\nabla f=
    \begin{pmatrix}
        x_1^{n-1} \\
        x_2^{n-1} \\
        \vdots \\
        x_n^{n-1} \\
    \end{pmatrix}
$$