If $x^2-x+1=0$, then value of $x^{3n}$ is

$(x+1)(x^2-x+1)=0(x-1)$

$\begin{array}{l}{x}^3+1=0\\ x^3=-1\\ \Rightarrow x=-1\\ {\left(x^3\right)}^n={(-1)}^n\end{array}$

$=-1\text{\hspace{0.17em}or\hspace{0.17em}}1$ (depends on 'n' )

(or)

$\begin{array}{l}-w,-w^2\\ \therefore x=-w\\ x^{3n}={\left(x^3\right)}^n={(-w^3)}^n\\ ={(-1)}^n\end{array}$

$=-1\text{\hspace{0.17em}or\hspace{0.17em}}1$ (depends on 'n' )