Quandaries
and Queries |
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I am a student secondary What is the ones digit of 3 to the 79 power? (hint: compute the first 12 powers of 3 and look for a pattern in the ones digits.) I have been trying for over 2 hours with this problem, I know it is probably a simple solution but for some reason I tend to over analyze and make it harder than it should be. If you can help I would be appreciative. Candice |
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Hi Candice, I'm going to compute powers of 3 and record them in a table but only record the ones digit.
What I see is that the ones digits are repeating in a pattern, 397139713971···. The pattern is 3971 and hence the pattern length is 4 digits.
79 divided by 4 is 19 with a remainder of 3 so the pattern would repeat 19 times and then there would be 3 more rows. The ones digits in these three rows are 3, 9 and 7 so the ones digit of 3 to the 79 is 7.
Penny |