Question

Find the unit's place in the expansion $3^{2006}$

Answer 1

The unit's place digit of $3^{2006}$

$\Rightarrow 3^1=3$; $3^2=9$ ; $3^3=27$ ; $3^4=81$

And thus the cycle of the unit's place is repeated after every $4^{th}$ power of $3$

$=$The unit's place digit of $3^{4\left(501\right)+2}$

$=$The unit's place digit of $3^2$

$=9$