Let's calculate the quotient: $$ \frac {3.3^{2.2}}{2.2^{3.3}} = \frac {3.3^{2.2}}{2.2^{2.2} \cdot 2.2^{\fbox{1.1}}} = \frac {(3/2)^{2.2}}{2.2^{1.1}} > \frac {1.5^2}{2.2^{1.1}} = \dots ? $$ EDIT: I edited out the shameful mistake, but now this calculation isn't useful. Oleg fixed it nicely, see below.

Let's calculate the quotient: $$ \frac {3.3^{2.2}}{2.2^{3.3}} = \frac {3.3^{2.2}}{2.2^{2.2} \cdot 2.2^{\fbox{1.1}}} = \frac {(3/2)^{2.2}}{2.2^{1.1}} > \frac {1.5^2}{2.2^{1.1}} = \dots ? $$ EDIT: I edited out the shameful mistake, but now this calculation isn't useful. Oleg fixed it nicely, see below.

Let's calculate the quotient: $$ \frac {3.3^{2.2}}{2.2^{3.3}} = \frac {3.3^{2.2}}{2.2^{2.2} \cdot 2.2} = \frac {(3/2)^{2.2}}{2.2} > \frac {1.5^2}{2.2} = \frac {2.25}{2.2} > 1 $$

Let's calculate the quotient: $$ \frac {3.3^{2.2}}{2.2^{3.3}} = \frac {3.3^{2.2}}{2.2^{2.2} \cdot 2.2^{\fbox{1.1}}} = \frac {(3/2)^{2.2}}{2.2^{1.1}} > \frac {1.5^2}{2.2^{1.1}} = \dots ? $$ EDIT: I edited out the shameful mistake, but now this calculation isn't useful. Oleg fixed it nicely, see below.