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fie a=9^2020-7^2020 ultima cifra a numarului a este

Răspuns :

[tex]\large{\underbrace{\underline{\bf{Întrebare}}}}:\\ [/tex]

  • Aflați ultima cifră a numărului a.

[tex]\large{\underbrace{\underline{\bf{Datele}}}}:\\ [/tex]

  • [tex] a = {9}^{2020} - {7}^{2020} [/tex]

[tex]\large{\underbrace{\underline{\bf{Rezolvare}}}}:\\ [/tex]

[tex] {9}^{2020} = ....? [/tex]

[tex] {9}^{1} = ......9 [/tex]

[tex] {9}^{2} = .........1 [/tex]

[tex] {9}^{3} = ..........9 [/tex]

[tex] {9}^{4} = ..........1 [/tex]

2020 ÷ 2 = 1010 rest 0

[tex]\color{blue}{9}^{2020} = .......1 [/tex]

[tex]\space[/tex]

[tex] {7}^{2020} = .....? [/tex]

[tex] {7}^{1} = .....7 [/tex]

[tex] {7}^{2} = .....9 [/tex]

[tex] {7}^{3} = ......3 [/tex]

[tex] {7}^{4} = .......1 [/tex]

[tex] {7}^{5} = ........7 [/tex]

etc.....

2020 ÷ 4 = 505 rest 0

[tex]\color{blue}{7}^{2020} = .......1 [/tex]

1 - 1 = 0

[tex]\color{red}\boxed{\boxed{{9}^{2020} - {7}^{2020} = ........0}}[/tex]