Question

find last 5 digit of 3^999​

Answer 1

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Answer 2

Answer:

number of last digit for nth power of n is in order 3,9,7,1

as in 3¹=3 3²=9(unit digit) 3³=7(Unit digit) 3⁴=1(unit digit) after this digits repeat as 3⁵=3(unit digit)

so unit digit repeat in intervals of four in 3⁹⁹⁹ dividing the power 999 by 4 we get 3 as remainder so the unit digit of 3⁹⁹⁹ will be 7