Question

calc ultima cifra a numerelor 2 la puterea 2018

Answer 1

Răspuns:

ultima cifra (2^2018)=u.c.(2^2)=4

2^1=2

2^2=4

2^3=8

2^4=16

2^5=32

observam ca se repeta din 4 in 4

2018:4=504(Rest2)

Answer 2

 

$\displaystyle\bf\\U(a^b)=notatia~pentru~ultima~cifra.\\\\U(2^{2018})=\\\\=U\Big(2^{2016+2}\Big)=\\\\=U\Big(2^{2016}\times2^2\Big)=\\\\=U\Big(2^{2016}\times2^2\Big)=\\\\=U\Big(2^{4\times504}\times2^2\Big)=\\\\=U\left(\Big(2^4\Big)^{504}\times2^2\right)=\\\\\\=U\Big(16^{504}\times2^2\Big)=\\\\=U\left(U\Big(6^{504}\Big)\times U\Big(2^2\Big)\right)=\\\\=U\Big(6\times 4\Big)=\\\\=U\Big(24\Big)=\boxed{\bf4}$