Showing the positivity of $p$-adic density of zeroes of a polynomial

Question

Let $f \in \mathbb{Z}[x_1, \ldots, x_n]$ and $p$ be a prime. Let $\nu_t(p)$ denote the number of solutions $\mathbf{x} \in ((\mathbb{Z}/p^t \mathbb{Z}))^*)^n$ to the congruence $$ f( \mathbf{x} ) \equiv 0 \pmod{p^t}. $$ We define (something similar to the $p$-adic density) $$ \mu(p) = \lim_{t \rightarrow \infty} \frac{ p^t \nu_t(p) }{ \phi(p^t)^n }. $$ Could someone please explain how to show $$ \mu(p) > 0 $$ provided the equation $f( \mathbf{x} ) = 0$ has a non-singular solution in $\mathbb{Z}_p^{\times}$, the units of $p$-adic integers? Thank you very much!