1.

Unit’s digit of any number that can be expressed as a power of any natural number between 1 and 9.Justify this statement.

Answer»

Unit’s digit of any number that can be expressed as a power of any natural number between 1 and 9:- 

(i) The units’ digit of any number expressed as a power of 2 is any of the digits 2, 4, 8, 6 as 21 = 2, 22 = 4, 23 = 8, 24 = 16, 25 = 32, ....... etc.

(ii) The units' digit of any number expressed as a power of 3 is any of the digits 3, 9, 7, 1 as 31= 3, 32= 9,33 = 27, 34 = 81, 35 = 243, ....... etc.

(iii) The units’ digit of any number expressed as a power of 4 is 4 if the power is odd and 6 if the power is even as 41 = 4, 42 = 16, 43 = 64, 44 = 256, ......etc.

(iv) The units' digit of any number expressed as a power of 5 is always 5 as 51 = 5, 52 = 25, 53 = 125, ........ etc

(v) The units' digit of any number expressed as a power of 6 is always 6 as 61 = 6, 62 = 36, 63 = 216, ........ etc.

(vi) The units' digit of any number expressed as a power of 7 is any of the digits 7, 9, 3, 1 as 71 = 7, 72 = 49, 73 = 343, 74 = 2401, ........ etc

(vii)The units' digit of any number expressed as a power of 8 is any of the digits 8, 4, 2, 6 as 81 = 8, 82 = 64, 83 = 512, 84 = 4096, ........ etc.

(viii) The units' digit of any number expressed as a power of 9 is 9 if the power is odd and 1 if the power is even as 91 = 9, 92 = 81, 93 = 729, 94 = 6561, ........ etc.



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