The veronese map $\nu_{n,d}: \mathbb{P}^n\longrightarrow \mathbb{P}^{{{d+n}\choose{n}}-1}$ is defined by $[...,x_j,...]\longrightarrow [...,M_k,...]$, where $M_k$ are all the monomials of degree $d$ in $\{...,x_j,...\}$. In the stackexchange post, Degrees of Veronese varieties, it is pointed out that the degree of the the image $\nu_{n,d}(\mathbb{P}^n)$, here called a Veronese variety, is given by $d^n$.
Question: What is the degree of $\nu_{n,d}(C)$, for any curve $C\subset \mathbb{P}^n$ of degree $a$?
Following the rational of the linked post, is this degree simply $ad^n$?
Yes. A hyperplane section of the Veronese variety is a hypersurface of degree $d^n$ in $\mathbb P^n$, so it intersects a curve of degree $a$ in $ad^n$ points.