which decimal digits occur as the final digit of a fourth power of an integer? S
ID: 2945380 • Letter: W
Question
which decimal digits occur as the final digit of a fourth power of an integer?Explanation / Answer
The last digit is only determined by the original last digit. (xxxxx0)^4 --> 0 x 0 x 0 x 0 --> 0 (xxxxx1)^4 --> 1 x 1 x 1 x 1 --> 1 (xxxxx2)^4 --> 2 x 2 x 2 x 2 --> 16 --> 6 (xxxxx3)^4 --> 3 x 3 x 3 x 3 --> 81 --> 1 (xxxxx4)^4 --> 4 x 4 x 4 x 4 --> 256 --> 6 (xxxxx5)^4 --> 5 x 5 x 5 x 5 --> 625 --> 5 (xxxxx6)^4 --> 6 x 6 x 6 x 6 --> 1296 --> 6 (xxxxx7)^4 --> 7 x 7 x 7 x 7 --> 2401 --> 1 (xxxxx8)^4 --> 8 x 8 x 8 x 8 --> 4096 --> 6 (xxxxx9)^4 --> 9 x 9 x 9 x 9 --> 6561 --> 1 Answer: The last digit will be an element of the set {0, 1, 5, 6}
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