Question

[English Study]

Tìm Chữ số tận cùng của lũy thừa:

7²⁰⁰⁸  ;   2³⁴⁵⁶ ;     204²⁰⁸   ; 9⁹⁶   ;  8¹⁹⁷⁵    ;    2003²⁰⁰⁷   ; 2022²⁰²²

Answer 1

[Nguyễn Thị Thương Hoài]

A = 7²⁰⁰⁸  = (7⁴)¹⁰⁰⁴ = (\(\overline{...1}\))¹⁰⁰⁴ = \(\overline{...1}\)

B = 2³⁴⁵⁶ = (2⁴)⁸⁶⁴ = \(\overline{...6}\)⁸⁶⁴ = \(\overline{...6}\)

C = 204²⁰⁸ = (204²)¹⁰⁴ = \(\overline{...6}\)¹⁰⁴ = \(\overline{...6}\)

D = 9⁹⁶ = (9²)⁴⁸ = \(\overline{...1}\) ⁴⁸ = \(\overline{...1}\)

E = 2003²⁰⁰⁷ = (2003⁴)⁵⁰¹.2003³ = \(\overline{...1}\) .\(\overline{..7}\) = \(\overline{..7}\)

G = 2022²⁰²² = (2022⁴)⁵⁰⁵.2022² = \(\overline{...6}\).\(\overline{...4}\)  = \(\overline{...4}\)

Answer 2

[Nguyễn Chí Dũng]

A = 72008  = (74)1004 = ($\overline{...1}$)1004 = $\overline{...1}$

B = 23456 = (24)864 = $\overline{...6}$864 = $\overline{...6}$

C = 204208 = (2042)104 = $\overline{...6}$104 = $\overline{...6}$

D = 996 = (92)48 = $\overline{...1}$ 48 = $\overline{...1}$

E = 20032007 = (20034)501.20033 = $\overline{...1}$ .$\overline{..7}$ = $\overline{..7}$

G = 20222022 = (20224)505.20222 = $\overline{...6}$.$\overline{...4}$  = $\overline{...4}$