How to solve in your head: 202 > 2^7, 303 < 2^9$202 > 2^7, 303 < 2^9$. Therefore 202^303 > 2^2121, 303^202 < 2^1818$202^{303} > 2^{2121}, 303^{202} < 2^{1818}$.
Even easier: 202^303 > 100^303 = 1000^202 > 303^202$202^{303} > 100^{303} = 1000^{202} > 303^{202}$.
