解:∵?$11^{10}$?的末尾數(shù)字為?$1,$??$22^{10}$?的末尾數(shù)字為?$4,$??$33^{10}$?的末尾數(shù)字為?$9$?
?$ 44^{10}$?的末尾數(shù)字為?$6,$??$55^{10}$?的末尾數(shù)字為?$5,$??$66^{10}$?的末尾數(shù)字為?$6$?
?$ 77^{10}$?的末尾數(shù)字為?$9,$??$88^{10}$?的末尾數(shù)字為?$4,$??$99^{10}$?的末尾數(shù)字為?$1$?
又∵?$1+4+9+6+5+6+9+4+1=45$?
∴所求式子的末位數(shù)字為?$5$?