What digit appears in unit place when $2^{320}$ is multiplied out  Is there a way to answer the following preferably without a calculator 


What digit appears in unit place when $2^{320}$ is multiplied out ? a)$0$ b)$2$ c)$4$ d)$6$ e)$8$
     ---- Ans(d)



Since $2^{320}$ is a square $2^{320}=(2^{150})^2$ and squares last digit is always $0,1,4,9,6,5$, two of them, $2$ and $8$, are ruled out. $0$ as well, since you need a $10$ for that. Write it as $(2^{75})^4$, and check that $4$th powers end with $0,1,6,1,6,5$ to get the remaining as result.
