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 

Bạn tham khảo nhé! Mình không chắc là đúng hay không nữa

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\(24^{54}.54^{24}.2^{10}=\left(2^3.3\right)^{54}.\left(3^3.2\right)^{24}.2^{10}\)\(=2^{3.54}.3^{54}.3^{3.24}.2^{24}.2^{10}\)
\(=2^{162}.3^{54}.3^{72}.2^{72}.2^{24}.2^{10}=2^{162+72+54+10}.3^{54+72}\)\(=2^{298}.3^{126}\).
\(72=3^3.2^3\)
\(72^{63}=\left(3^3.2^3\right)^{63}=3^{189}.2^{189}\)
Như vậy đề bài sai.

XIN NỖI TOÁN 6

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

 24⁵⁴.54²⁴.2¹⁰ = (2³.3)⁵⁴.(2.3³)²⁴.2¹⁰ = 2¹⁶².3⁵⁴.2²⁴.3⁷².2¹⁰ = 2¹⁹⁶.3¹²⁶ = 2⁷(2¹⁸⁹.3¹²⁶) = 2⁷.[(2³)⁶³.(3²)⁶³] = 2⁷.(8⁶³.9⁶³) = 2⁷.72⁶³ chia hết cho 72⁶³

Tính: (1 - 1/4 ) . (1 - 1/9) . (1 - 1/16) ... (1 - 1/81) . (1 - 1/100)

-Ta có:

+\(72^{63}=\left(2^3\cdot3^2\right)^{63}=\left(2^3\right)^{63}\cdot\left(3^2\right)^{63}=2^{189}\cdot3^{126}\)

+\(24^{54}\cdot54^{24}\cdot2^{10}\)

=\(\left(2^3\cdot3\right)^{54}\cdot\left(2\cdot3^3\right)^{24}\cdot2^{10}\)

=\(2^{162}\cdot3^{54}\cdot2^{24}\cdot3^{72}\cdot2^{10}\)

=\(2^{196}\cdot3^{126}\)

=\(2^7\cdot2^{189}\cdot3^{126}\)             

Vì \(2^7\cdot2^{189}\cdot3^{126}⋮2^{189}\cdot3^{126}\) 

\(\Rightarrow24^{54}\cdot54^{24}\cdot2^{10}⋮2^{63}\)                                                                                                                                                   

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

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

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

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

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

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