Question

[Nguyễn Nguyệt Hà]

Cmr 24⁵⁴  . 54²⁴.2¹⁰  chia hết cho 72⁶³ 

 ^{nhanh nha ai nhanh nhát ninh se tik ma phai dung}

Answer 1

[Hoàng Thảo Linh]

ta có:

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

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

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

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

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

mà \(72^{63}=\left(2^3.3^2\right)^{63}=\left(2^3\right)^{63}.\left(3^2\right)^{63}=2^{189}.3^{126}\)

lại có :\(2^{196}.3^{126}\)  chia hết cho \(2^{189}.3^{126}\)

\(\Rightarrow24^{54}.54^{24}.2^{10}\)   chia hết cho \(72^{63}\)