# 我有個有關數學上的難題

7的40次方，個位數是甚麼，十位數又是什麼?

### 5 個解答

• 匿名使用者
1 0 年前
最佳解答

個位數是1

十位數是0

7的1次方=7

7的2次方=49

7的3次方=343

7的4次方=2401

7的5次方=16807

7的6次方=.....649

7的7次方=........43

最後你不需要乘到百位以上

因為用不到

你會發現

他是四個一循環的

這種題目一定是有規律

他才會問

參考資料： 自己
• dd
Lv 6
1 0 年前

72-1 ≡ 71 ≡ 1 (mod 2)75-1 ≡ 74 ≡ 1 (mod 5)74 ≡ 1 (mod 10)74-1 ≡ 0 (mod 10)(74-1)2 ≡ 0 (mod 100)78-2*74+1 ≡ 0 (mod 100)78 ≡ 2*74-1 (mod 100)78 ≡ 2*2401-1 ≡ 2*1-1 ≡ 1 (mod 100)740 ≡ (78)5 ≡ 15 ≡ 1 (mod 100)所以個位數=1十位數=0

• 匿名使用者
1 0 年前

7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

49*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

343*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

2401*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

16807*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

117649*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

823543*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

5764801*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

40353607*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

282475249*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

1977326743*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

13841287201*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

96889010407*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

678223072849*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

4747561509943*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

33232930569601*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

232630513987207*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

1628413597910449*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

11398895185373143*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

79792266297612001*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

558545864083284007*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

3909821048582988049*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

27368747340080916343*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

191581231380566414401*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

1341068619663964900807*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

9387480337647754305649*7*7*7*7*7*7*7*7*7*7*7*7*7*7=

65712362363534280139543*7*7*7*7*7*7*7*7*7*7*7*7*7=

489986536544739960976801*7*7*7*7*7*7*7*7*7*7*7*7=

3219905755813179726837607*7*7*7*7*7*7*7*7*7*7*7=

22539340290692258087863249*7*7*7*7*7*7*7*7*7*7=

157775382034845806615042743*7*7*7*7*7*7*7*7*7=

1104427674243920646305299201*7*7*7*7*7*7*7*7=

7730993719707444524137094407*7*7*7*7*7*7*7=

54116956037952111668959660849*7*7*7*7*7*7=

378818692265664781682717625943*7*7*7*7*7=

265173084585965347177902381601*7*7*7*7=

18562115921017574302453163671207*7*7*7=

129934811447123020117172145698449*7*7=

909543680129861140820205019889143*7=

6366805760909027985741435139224001

個位數為1

十位數為0

參考資料： 自己算
• 1 0 年前

7的1次方 個位數是7

7的2次方 個位數是9

7的3次方 個位數是3

7的4次方 個位數是1

7的5次方 個位數是7

以此類推 7的40次方 個位數是1

• 您覺得這個回答如何？您可以登入為回答投票。
• 1 0 年前

Anny說的對...

順帶一提...如果看到有很高的次方時通常都是有規律ㄉ