<s>[INST] Which numbers is bigger $80^{105}$ or $28^{140}$ 
Which numbers is bigger   $80^{105}$ or $28^{140}$

My try follows  
$80^{105}$ = $(80^{3})^{35}$=$(512000)^{35}$
$28^{140}$=$(28^{4})^{35}$=$ (614656)^{35}$
So $28^{140}$ is bigger 
Is there another idea for this problem involving relations between $80$ and $81$  and $27$ and $28$  since  $81$ and $27$  have common base $3$
Thank you for your help 
 [/INST] As $(105,140)=35$
we can check  for $80^3,28^4$
$80^3=(5\cdot2^4)^3=5^32^{12},28^4=(7\cdot2^2)^4=7^4\cdot2^8$
$80^3>=<28^4\iff5^32^{12}>=<7^4\cdot2^8\iff5^32^4>=<7^4$
Now $7^4=2401,5^32^4=2\cdot10^3=2000$
</s>