Question

Determină ultima cifra a numărului.
a) 3 la puterea 59
b) 4 la puterea 52
c) 6 la puterea 156
d) 7 la puterea 2017

Answer 1

$u \: 3 {}^{59} \\ 3 {}^{1} = 3 \\ 3 {}^{2} = 9 \\ 3 {}^{3} = 27 \\ 3 {}^{4} = 81 \\ 3 {}^{5} = 243 \\ \\ 59 \div 4 = 14r3 \\ \\ u3 {}^{56} = u \: (3 {}^{3} ) = 7$



$u \: 4 {}^{52} \\ 4 {}^{1} = 4 \\ 4 {}^{2} = 16 \\ 4 {}^{3} = 64 \\ \\ 52 \div 4 = 13 \\ \\ u \: 4 {}^{52} = u \: (4 {}^{0} ) = 1$



$u6 {}^{156} \\ 6 {}^{1} = 6 \\ 6 {}^{2} = 36 \\ \\ 156 \div 4 = 39 \\ \\ u \: 6 {}^{156} = u(6 {}^{0} ) = 1$



$u7 {}^{2017} \\ \\ 7 {}^{1} = 7 \\ 7 {}^{2} = 49 \\ 7 {}^{3} = ..3 \\ 7 {}^{4} = ..1 \\ 7 {}^{5} = ..7 \\ \\ 2017 \div 4 = 54r1 \\ \\ u7 {}^{2017} = \: u(7 {}^{1} ) = 7$


Succes !