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Question Number 19389 by tawa tawa last updated on 10/Aug/17
What is the digital root of  3^(2017)
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{digital}\:\mathrm{root}\:\mathrm{of}\:\:\mathrm{3}^{\mathrm{2017}} \\ $$
Answered by allizzwell23 last updated on 10/Aug/17
   1×9 = 9     2×9 = 18 = 1+8 = 9     3×9 = 27 = 2+7 = 9    .............     3^(2017)  = 3^(2015) ×9  = 9    Hence, the digital root is 9
$$\:\:\:\mathrm{1}×\mathrm{9}\:=\:\mathrm{9} \\ $$$$\:\:\:\mathrm{2}×\mathrm{9}\:=\:\mathrm{18}\:=\:\mathrm{1}+\mathrm{8}\:=\:\mathrm{9} \\ $$$$\:\:\:\mathrm{3}×\mathrm{9}\:=\:\mathrm{27}\:=\:\mathrm{2}+\mathrm{7}\:=\:\mathrm{9} \\ $$$$\:\:…………. \\ $$$$\:\:\:\mathrm{3}^{\mathrm{2017}} \:=\:\mathrm{3}^{\mathrm{2015}} ×\mathrm{9}\:\:=\:\mathrm{9} \\ $$$$\:\:\mathrm{Hence},\:\mathrm{the}\:\mathrm{digital}\:\mathrm{root}\:\mathrm{is}\:\mathrm{9} \\ $$
Commented by tawa tawa last updated on 10/Aug/17
God bless you sir.
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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