XIN NỖI TOÁN 6

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

ta có: \(72^{63}=9^{63}.8^{63}=\left(3^2\right)^{63}.\left(2^3\right)^{63}=3^{72}.2^{108}\)

ta có: \(\frac{3^{126}.2^{196}}{3^{72}.2^{108}}=3^{54}.2^{88}\)

suy ra \(3^{126}.2^{196}\) chia hết cho \(3^{72}.2^{108}\)

suy ra \(24^{54}.54^{24}.2^{10}\) chia hết cho \(72^{63}\)

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!!!

24^54 x 54^24 x 2^10=(2^3.3)^5 x (3^3.2)^24... 

=(2^3)^54 x 3^54 x (3^3)^24 x 2^24 x 2^10 

= 2^162 x 2^24 x 2^10 x 3^54 x 3^72 

=2^196 x 3^126 

72^63=(2^3 x 3^2)^63 

=(2^3)^63 x (3^2)^63= 2^18 x 3^126 

Vì  2^196 x 3^126 chia hết 2^189 x 3^126 

=>24^54 x 54^24 x 2^10 chia hết 72^63