Question

cmr

81^7 - 27^9 - 9^13\(⋮\) 15

24^54 . 54^24 . 2^10\(⋮\) 72^63

Answer 1

a, Ta có:

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

\(=3^{26}\left(3^2-3-1\right)=3^{25}.3.5=3^{25}.15\)

Vì 15 chia hết cho 15 nên \(3^{25}.15\) chia hết cho 15.

Vậy................(đpcm)

b,Ta có:

\(24^{54}.54^{24}.2^{10}=\left(2^3.3\right)^{54}.\left(2.3^3\right)^{24}.2^{10}\)

\(=2^{162}.3^{54}.2^{24}.3^{72}.2^{10}=2^{196}.3^{126}\)

\(=2^{108}.3^{72}.2^{88}.3^{54}\)

\(72^{36}=\left(2^3.3^2\right)^{36}=2^{108}.3^{72}\)

Vì \(2^{108}.3^{72}\) chia hết cho \(2^{108}.3^{72}\) nên \(2^{108}.3^{72}.2^{88}.3^{54}\) chia hết cho \(2^{108}.3^{72}\)

Vậy............(đpcm)

Chúc bạn học tốt!!!