Question

Aflați ultima cifră a unui nr.2^57;4^93;7^33;5^69...unde" ^"=putere

Answer 1

   
[tex]U(2^{57}) = U(2^{56+1})= U(2^{56}\times 2) =U(2^{4\times 14}\times 2)= \\ =U((2^{4})^{14}\times 2)=U(16^{14}\times 2)=U(6\times 2)=U(12)=\boxed{2} \\ \\ \\ U(4^{93})= U(4^{90+3})=U(4^{90}\times 4^3})=U(4^{2 \times 45}\times 4^3})=U((4^2)^{45}\times 4^3})= \\ =U(16^{45}\times 4^3})= U(16^{45}\times 64})=U(6 \times 4) = U(24)=\boxed{4}[/tex]


[tex]U(7^{33}) = U(7^{32+1}) =U(7^{4\times 8+1}) =U((7^{4})^8\times 7^1 }) = \\ =U(2401^8\times 7^1}) =U(1 \times 7) = \boxed{7}[/tex]


$U(5^{69}) = \boxed{5} ~~~\text{ deoarece 5 la orice putere are uultima cifra 5}$