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Find the units digit of 13^19 *19 ^13

 

I already tried an answer but got it wrong. Can someone please explain how to do this problem?

 Aug 7, 2023

Best Answer 

 #1
avatar+183 
+3

The units digit for powers of three is: 3,9,7,1,3... The 19th number will be 7.

 

The pattern for 9 is: 9,1,9... and the thirteenth number will be 9

 

Then we have 7*9, which has a units digit of 3

 Aug 7, 2023
 #1
avatar+183 
+3
Best Answer

The units digit for powers of three is: 3,9,7,1,3... The 19th number will be 7.

 

The pattern for 9 is: 9,1,9... and the thirteenth number will be 9

 

Then we have 7*9, which has a units digit of 3

plaintainmountain Aug 7, 2023
 #2
avatar+126978 
+2

Powers of 13 (starting with 13^1) end in

3, 9, 7, 1    a cycle of  4

So

13^19  ends in 7

 

Powers of 19  (starting with 19^1) end in

9, 1      a cycle of 2

So

19^13  ends in 9

 

So

 

13^19 * 19^13  ends in

7  * 9  =     ...3

 

cool cool cool

 Aug 8, 2023

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