Since this is a discrete signal, and n can take only values like ...,1,2,3 ... the value of the power is getting zero, and since it gets zero does it mean that it's not a power signal?
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There a few variations on the definitions of "energy signal" and "power signal". For example, Sklar in his textook "Digital Communications" defines "energy signal" as a signal with energy $E$ such that $0 < E < \infty$, and a "power signal" as a signal with power $P$ such that $0 < P <\infty$.
However, others (see for example this answer) define "energy signal" as a signal with $E < \infty$.
In your case, $x[n]=0$ for all $n$; then this signal has zero energy and zero power. Whether it is classified as an energy or a power signal depends on which specific definition you adopt. For instance, if you go with Sklar's, then this signal is neither an energy signal nor a power signal.