Quandaries and Queries
  

 

the level of the question: Precalculus (grade 10)
who is asking the question: Student

Question: If 2 to the power of 31921 is multiplied out, what will be the units digit?

Thank you!

 

 

Hi,

Start to calculate powers of 2 and watch the units digit

Power of 2 Units digit
2 1 2
2 2 4
2 3 8
2 4 6
2 5 2
2 6 4
2 7 8
2 8 6
2 9 2

Do you see what's happening? The units digits column is repeating in cycles of length 4,

2486 2486 2...

If you continue this list for 31921 rows how many cycles of length 4 will there be? How many more rows are there after that? What is the units digit in the 31921th row?

Cheers,
Penny 		 
 

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