1^100 = 1.Trevially the digit in unit place is 1
2^100= (2^4)^25 = (26)^26 digit in ones place is like that in6^25 in ones digit=6 in units or ones place.
3^100 = (3^4)25=(81)^25 = ends in ones place like 1^25 = 1, has 1 in its unit place
4^100=(4^2)50= 16^50= ends inunit place like 6^50 . Ending in 6 in ones place .
5^100 : Any positive integral power obviously inthis number has 5 in its ones digit.
6^100: has obviously 6 in its ones digit.
7^100= (7^4)^25=(2401)^25 behaves like 1^25 for its ones digit.Therefore has 1 in its ones digit.
8^10=(8^4)^25=(4096)^6. This number shall have its ones digit as in 6^25, which has 6 in units place.
9^100=(81)^50. This number has ones digit like 1^25. Therefore it has 1 in unit digit
10^100, has obviously has 0 in ones digit.
Therefore, 1^100, 3^100,7^100 and 9^100 - These odd numbers or any odd number like this in units place to the power of 100 have 1 in ones digit.
2^100, 4^100, 6^100 qnd 8^100 ---These even numers or any even number like this in unit place to the power of 100 has 6 in ones digit.
10^100-This even number or any even number with zero in ones digit to the power of 100 has 0 in its ones place.
5^100; This number or any integer with 5 in its ones place to the power of 100 has 5 in ones digit.
Hope this helps.
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