Factorize each composite base:
[tex]24=2^3\cdot3[/tex]
[tex]54=2\cdot3^3[/tex]
[tex]72=2^3\cdot3^2[/tex]
Then
[tex]24^{54}=2^{162}\cdot3^{54}[/tex]
[tex]54^{24}=2^{24}\cdot3^{72}[/tex]
[tex]72^{63}=2^{189}\cdot3^{126}[/tex]
Now cancel as many factors as possible:
[tex]\dfrac{24^{54}\cdot54^{24}\cdot2^{10}}{72^{63}}=\dfrac{2^{196}\cdot3^{126}}{2^{189}\cdot3^{126}}=2^7[/tex]
The denominator vanishes, so [tex]72^{63}[/tex] does divide [tex]24^{54}\cdot54^{24}\cdot2^{10}[/tex].
