Question

[Trần Thanh Hằng]

1) Chứng tỏ rằng:  81^{7 _}  27^{9 _} 9¹³ chia hết cho 405.

Answer 1

[Trần Đức Thắng]

\(81^7-27^9-9^{13}=3^{4.7}-3^{3.9}-3^{2.13}=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\left(3^2-3-1\right)=3^{26}.5=3^{22}.3^4.5=3^{22}.81.5=405.3^{22}\)

Chia hết cho 405 => ĐPCM

Answer 2

[Hồ Nguyện]

81⁷= (3⁴⁾⁷  = 3^4.7