Question

[Chuột yêu Gạo]

Chứng minh rằng;

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

Answer 1

[Nguyễn Thanh Hằng]

\(24^{54}.54^{24}.2^{10}\)

\(=\left(2^3.3\right)^{54}.\left(3^3.2\right)^{24}.2^{10}\)

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

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

\(=2^{196}.3^{126}\)

Lại có :

\(72^{63}=\left(2^3.3^2\right)^{63}\)

\(=\left(2^3\right)^{63}.\left(3^2\right)^{63}\)

\(=2^{189}.3^{126}\)

Vì \(2^{196}.3^{126}⋮2^{189}.3^{126}\Leftrightarrowđpcm\)