Finding last digits of 983389^389

[Alexthexela]

Posted is a discrete mathematics problem. I'm having trouble with step 2, where I'm instructed to "reduce the base." Does this refer to the logarithmic base? I'm looking through my textbook and at help articles online, but still finding myself confused. I'm new to this type of problem and seeking advice on this spot in particular, but any guidance you can provide would be much appreciated. Thank you all.View attachment 8063

 

[Opalg]

Posted is a discrete mathematics problem. I'm having trouble with step 2, where I'm instructed to "reduce the base." Does this refer to the logarithmic base? I'm looking through my textbook and at help articles online, but still finding myself confused. I'm new to this type of problem and seeking advice on this spot in particular, but any guidance you can provide would be much appreciated. Thank you all.

Hi Alexthexela, and welcome to MHB!

In the number $983,389^{389}$, the base is $983,389$ and the exponent is $389$. The problem tells you to "think (mod 1000)". To do that, the first step is to "reduce the base" (mod 1000), in other words to replace $983,389$ by $389$. The reason for doing that is that the last three digits of $389^{389}$ will be the same as the last three digits of $983,389^{389}$. That is all there is to step 2 of the problem, and you can then move on to step 3.