[tex]72^{63}\\\\72=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^4\cdot3^2\\\\72^{63}=(2^4\cdot3^2)^{63}=(2^4)^{63}(3^2)^{63}=2^{152}\cdot3^{126}[/tex]
[tex]24^{54}\cdot54^{24}\cdot2^{10}\\\\24=2\cdot2\cdot2\cdot3=2^3\cdot3\\54=2\cdot3\cdot3\cdot3=2\cdot3^3\\\\24^{54}=(2^3\cdot3)^{54}=(2^3)^{54}\cdot3^{54}=2^{162}\cdot3^{54}\\\\54^{24}=(2\cdot3^3)^{24}=2^{24}\cdot(3^3)^{24}=2^{24}\cdot3^{72}\\\\24^{54}\cdot54^{24}\cdot2^{10}=2^{162}\cdot3^{54}\cdot2^{24}\cdot3^{72}=2^{162+24}\cdot3^{54+72}=2^{186}\cdot3^{126}\\\\=2^{34+152}\cdot3^{126}=2^{34}\cdot\underbrace{2^{152}\cdot3^{126}}_{72^{63}}=2^{34}\cdot72^{63}[/tex]
[tex]24^{54}\cdot54^{24}\cdot2^{10}=2^{34}\cdot72^{63}\\\\\text{therefore it is divisible by}\ 72^{63}[/tex]
[tex]Used:\\\\(ab)^n=a^nb^m\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}[/tex]
