1. Ta có: \(16^{30}=\left(2^4\right)^{30}=2^{120}\)
Mà \(2^{120}< 3^{120}< 3^{121}\)
\(\Rightarrow2^{120}< 3^{121}\)
\(\Rightarrow16^{30}< 3^{121}\)
2. Ta có: \(5^{22}=5^{2.11}=\left(5^2\right)^{11}=25^{11}\)
Vì 25 < 64 nên \(25^{11}< 64^{29}\)
Vậy \(5^{22}< 64^{29}\)
3. Ta có: \(8^{120}=\left(2^3\right)^{120}=2^{360}\)
\(64^{29}=\left(2^6\right)^{29}=2^{174}\)
Vì 360 < 174 nên \(2^{360}< 2^{174}\)
Vậy \(8^{120}>64^{29}\)
4. Ta có: \(333^{444}=\left(333^4\right)^{111}\) \(=\left(111^4.3^4\right)^{111}=\left(111^4.81\right)^{111}\)
\(444^{333}=\left(444^3\right)^{111}\) \(=\left(111^3.4^3\right)^{111}=\left(111^3.64\right)^{111}\)
Vì \(111^4.81>111^3.64\) nên \(\left(111^4.81\right)^{111}>\left(111^3.64\right)^{111}\)
Vậy \(333^{444}>444^{333}\)
