Is there any rule for powers so that i can compare which one is greater without actually calculating? For example
54^53 and 53^54 23^26 and 26^23 3^4 and 4^3 (very simple but how without actually calculating)
If $a\gt b\gt e , b^a\gt a^b$. To see this, take logs. You want to compare $a \ln b$ with $b \ln a$. $\ln$ rises slowly, so the larger multiplier wins.