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Find the last digit of 196^213 · 213^196 .

 May 15, 2021
 #1
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CPhill plsss helppp

 May 15, 2021
 #2
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anyone plsss

Guest May 15, 2021
 #4
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I'm  here, guest :- )

MathProblemSolver101  May 15, 2021
 #3
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Last digit of $196^{213}:$

We only need to care about the last digit. That is $6.$

We notice a repetition in the last digit of every $6^{n}$: it is $6.$

Now, last digit of $213^{196}:$

Similarily, we notice a repetition between $3^{1,2,3,4}:$ it is $3, 9, 7, 1.$

$196$ is a multiple of $4$ so the last digit is $1.$

 

$6 \cdot 1 = \boxed{6}.$

 May 15, 2021
 #5
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Well Explained Bro :)

mathisopandcool  May 15, 2021

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