Ta có:a)\(^{3^{600}}\)=\(^{\left(3^3\right)^{200}}\)=\(^{27^{200}}\) \(^{4^{400}}\)=\(^{\left(4^2\right)^{200}}\)=\(^{16^{200}}\)
vì 27^200>16^200 => 3^600>4^400
b) \(^{4^{32}=4^{2.16}=16^{16}}\) vì 16^16>16^15 => 4^32>16^15
\(3^{600}=3^{200.3}=\left(3^3\right)^{200}=9^{200}^{_{\left(1\right)}}\)
\(4^{400}=\left(2^2\right)^{400}=2^{800}=2^{200.4}=\left(2^4\right)^{200}=16^{200}_{\left(2\right)}.\)
\(\left(1\right),\left(2\right)\Rightarrow4^{400}>3^{600}\)
\(4^{32}=\left(2^2\right)^{32}=2^{64}_{\left(1\right)}\)
\(16^{15}=\left(2^4\right)^{15}=2^{60}_{\left(2\right)}\)
\(\left(1\right),\left(2\right)\Rightarrow4^{32}>16^{15}\)