Question

Comparati $2^{4410}$ si $6^{945}$

Answer 1

2⁴⁴¹⁰ = ( 2¹⁴ )³¹⁵ = ( 2⁷ 2⁷ )³¹⁵ = ( 128 · 128 )³¹⁵ 
6⁹⁴⁵ = ( 6³ )³¹⁵   = 216³¹⁵ 
     ⇒      6⁹⁴⁵  <  2⁴⁴¹⁰ 

Answer 2

$2^{4410}=(2 ^{14}) ^{315}=( 2^{7}* 2^{7}) ^{315}=(128*128) ^{315} = \ \textgreater \ 16384^{315} \\ 6^{945}=( 6^{3}) ^{315} = \ \textgreater \ 216^{315} \\ 6 ^{945}\ \textless \ 2^{4410}$