The sum of

$x^{3}-2 x^{2}+2 x-1=0$

$x=1$ satisfying the equation

$\therefore \mathrm{x}-1$ is factor of

$x^{3}-2 x^{2}+2 x-1$.

$=(x-1)\left(x^{2}-x+1\right)=0$

$x=1, \frac{1+i \sqrt{3}}{2}, \frac{1-i \sqrt{3}}{2}$

$x=1,-\omega^{2},-\omega$

sum of $162^{\text {th }}$ power of roots

$=(1)^{162}+\left(-\omega^{2}\right)^{162}+(-\omega)^{162}$

$=1+(\omega)^{324}+(\omega)^{162}$

$=1+1+1=3$