The sum of 162^th power of the roots of the equation x³ $-$ 2x² + 2x $-$ 1 = 0 is ________.

x³ $-$ 2x² + 2x $-$ 1 = 0<br><br>x = 1 satisfying the equation<br><br>$\therefore$ x $-$ 1 is factor of <br><br>x³ $-$ 2x² + 2x $-$ 1<br><br>= (x $-$ 1) (x² $-$ x + 1) = 0<br><br>x = 1, ${{1 + i\sqrt 3 } \over 2},{{1 - i\sqrt 3 } \over 2}$<br><br>x = 1, $-$ $\omega$², $-$$\omega$<br><br>Sum of 162^th power of roots<br><br>= (1)¹⁶² + ($-$$\omega$²)¹⁶² + ($-$$\omega$)¹⁶²<br><br>= 1 + ($\omega$)³²⁴ + ($\omega$)¹⁶²<br><br>= 1 + 1 + 1 = 3