The sum  of ${162}^{th}$ power of the roots of the equation  $x^3-2x^2+2x-1=0$is  

The given equation is $x^3-2x^2+2x-1=0$

$( x^3-1)-2x\left(x-1\right)=0$

$\begin{array}{l}(x-1)\left(x^2-x+1\right)=0\\ x=1,x=-w,-w^2\\ {\alpha }^{162}+{\beta }^{162}+{\gamma }^{162}=1+{\left(w^3\right)}^{54}+{\left(w^6\right)}^{54} =1+1+1=3\end{array}$

The value is 3.