a. \(3^{200}= \left(3^2\right)^{100}=9^{100}\)

\(2^{300}=\left(2^3\right)^{100}=8^{100}\)

Vì 9 > 8 nên 9 ¹⁰⁰ > 8¹⁰⁰

Vậy 3²⁰⁰ > 2³⁰⁰.

b. \(333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)

\(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)

Vì 81¹¹¹ > 64¹¹¹ và 111⁴⁴⁴ > 111³³³ nên \(81^{111}.111^{444}>64^{111}.111^{333}\)

Vậy 333⁴⁴⁴ > 444³³³.

c. \(3^{54}=\left(3^2\right)^{27}=9^{27};2^{81}=\left(2^3\right)^{27}=8^{27}\)

Vì 9 > 8 nên 9²⁷ > 8²⁷

Vậy 3⁵⁴ > 2⁸¹.