7×7×7×…×7
50個(gè)
 所得積末位數(shù)是
9
9
分析:當(dāng)7的個(gè)數(shù)是1時(shí),末位是7;當(dāng)7的個(gè)數(shù)是2時(shí),末位是9;當(dāng)7的個(gè)數(shù)是3時(shí),末位是3;當(dāng)7的個(gè)數(shù)是4時(shí),末位是1;當(dāng)7的個(gè)數(shù)是5時(shí),末位又是7;由此發(fā)現(xiàn)積的末尾依次出現(xiàn)7、9、3、1;依此規(guī)律解答即可.
解答:解:先找出積的末位數(shù)的變化規(guī)律:
71末位數(shù)為7,72末位數(shù)為9,73末位數(shù)為3,74末位數(shù)1;75=74+1末位數(shù)為7,76=74+2末位數(shù)為9,77=74+3末位數(shù)為3,78=74×2末位數(shù)為1;
由此可見(jiàn),積的末位依次為7,9,3,1,7,9,3,1,以4為周期循環(huán)出現(xiàn).
因?yàn)?0÷4=12…2,即750=74×12+2,所以750與72末位數(shù)相同,也就是積的末位數(shù)是9.
故答案為:9
點(diǎn)評(píng):此題考查的目的是:通過(guò)計(jì)算發(fā)現(xiàn)規(guī)律,依照規(guī)律解答這類(lèi)問(wèn)題.
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