Unit digit of the number (22)²³ is :

$$\eqalign{ & {\left( {22} \right)^{23}} \cr & {\text{ Result unit digit}} \cr & {2^1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,2\, \leftarrow | \cr & {2^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,|\,\,{\text{Cycle}} \cr & {2^3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,\,\,\,\,\,\,|\,\,\,{\text{Completes}} \cr & {2^4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,16\,\,\,\,\,\,\,\,\,\,\,\,6 \leftarrow \,| \cr & {2^5}\,\,\,\,\,\,\,\,\,\,\,\,\,32\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\, \cr & {\text{So divided power of 22 by 4 }} \cr & \frac{{23}}{4} = {\text{ remainder 3}} \cr & {2^3}\,\,\,\, = \,\,\,\,\,8\, \cr & {\text{unit digit = 8}} \cr} $$