24^54.54^24.2^10=(2^3.3)^54.(3^3.2)^24... 

=(2^3)^54.3^54.(3^3)^24.2^24.2^10 

= 2^162.2^24.2^10.3^54.3^72 

=2^196.3^126 

72^63=(2^3.3^2)^63 

=(2^3)^63(.3^2)^63=2^189.3^126 

vì 2^196.3^126 chia hết 2^189.3^126 

=>24^54.54^24.2^10 chia hết 72^63 

Cảm ơn bạn nhìu lắm.Mình cho luôn **** rồi nhé

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

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

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

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

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

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

mk ko bt 123

Ta có:

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

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

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

\(=2^{196}.3^{126}\) (1)

Lại có:

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

Từ (1) và (2) ⇒ \(24^{54}.54^{24}.2^{10}⋮72^{63}\)

tham khảo câu b bài 1 ở link này https://olm.vn/hoi-dap/detail/88152567739.html

b) dễ lắm cậu tự làm nha , tách ra thành 2 vế rồi rút gọn lại

c) \(3^{n+2}-2^{n+2}+3^n-2^n\)

\(=3^n.9-2^n.4+3^n.1-2^n.1\)

\(=3^n.\left(9+1\right)-2^n.\left(4+1\right)\)

\(=3^n.10-2^n.5\)

\(=3^n.10-2^{n-1}.2.5\)

\(=3^n.10-2^{n-1}.10\)

\(=10.\left(3^n.2^{n-1}\right)\)