MHB Finding last digits of 983389^389

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To find the last digits of 983389^389, the base should be reduced modulo 1000, meaning you replace 983389 with 389. This simplification is crucial because the last three digits of 389^389 will match those of 983389^389. The confusion regarding "reducing the base" does not pertain to logarithmic bases but rather to modular arithmetic. Once the base is reduced, the next steps in the problem can be pursued. Understanding this reduction is key to solving the discrete mathematics problem effectively.
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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
 

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Alexthexela said:
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.
 
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