Experiences can answer this.

I WARN YOU THAT THIS IS NOT A GENERAL METHOD!! BUT COULD BE APPLIED IN MANY SUCH CASES. Here the magnitude of the number ( 2132 and 2386 ) have a large difference ( at-least that is greater than 200 !!)

Let a = $2132^{2386}$ and b = $2386^{2132}$

Calculate the value of log ( a ) and log ( b ) . The bigger the value is of any of the two numbers would mean that the larger is the number actually from the other

By the way the value of the " log " of two numbers would only tell you the number of digits the number contains .Here I have taken log to bare 10.

log ( a ) = 2386 log ( 2132 ) = 7942.48 log ( b ) = 2132 log ( 2368 ) = 7194.18

The number b has 748 digits less ( Place Value) and so it surely tells us that a > b

This is how i think ! Example : I have a small no. like : 2 and 5 ( I will take this 2 no. to make an example ) You do it with the same formula like the question of Adam : 2^5 .... 5^2 5^2 = 25 2^5 = 32 => 2^5 > 5^2 Ok, done =)