Aflati ultima cifră a numărului:
a) 3^2019 + 5^2020 + 1^2021;
b) 2^2019 + 6^2020 + 2019^0;
C) 4^2019 + 7^2020 + 8^2021 – 9^2022.
Răspunsuri la întrebare
Răspuns:
a) 3^2019 + 5^2020 + 1^2021
Mai intai aflam ultima cifra a fiecarui numar:
3¹=3; 3²=9; 3³=27; 3⁴=81; 3⁵=...3
2019:4=504 rest 3
3²⁰¹⁹= ...7
5¹=5: 5²=25; 5³=...5
5²⁰²⁰=....5
1²⁰²¹= 1
7+5+1=13; ultima cifra =3
b) 2^2019 + 6^2020 + 2019^0
Mai intai aflam ultima cifra a fiecarui numar:
2¹=2; 2²=4; 2³=8; 2⁵=32; 2⁶=...4
2019: 3= 673 rest 0
2²⁰¹⁹= ...8
6¹=6; 6²=36; 6³=...6
6²⁰²⁰=...6
2019⁰=1
8+6+1=15; ultima cifra=5
c) 4^2019 + 7^2020 + 8^2021 – 9^2022
Mai intai aflam ultima cifra a fiecarui numar:
4¹=4; 4²=16; 4³=64; 4⁴=...6
2019:2=1009 rest 1
4²⁰¹⁹=...4
7¹=7; 7²=49; 7³=..3; 7⁴=...1; 7⁵=...7
2020:4=505 rest 0
7²⁰²⁰=...1
8¹=8; 8²=64; 8³=...2; 8⁴=...6; 8⁵=...8
2021:4=505 rest 1
8²⁰²¹=...8
9¹=9; 9²=81; 9³=...9
2022:2=1011 rest 0
9²⁰²²=...1
4+1+8-1=12; ultima cifra=2
Sper ca te-am ajutat!