The unit digit of {{21}^{32}}+{{32}^{43}}+{{43}^{54}}+{{54}^{65}} is .
{{21}^{32}}+{{32}^{43}}+{{43}^{54}}+{{54}^{65}}\equiv {{1}^{32}}+{{2}^{43}}+{{3}^{54}}+{{4}^{65}}(\bmod 10)
\equiv 1+{{2}^{3}}+{{3}^{2}}+{{4}^{1}}(\bmod 10)
\equiv 1+8+9+4(\bmod 10)
\equiv 2(\bmod 10)．
