power of 101

Algebra Level 2

Find the units digit of 39^101

3 1 7 0 9 2 6 5

Evan Hong by Evan Hong , 30, USA

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4 solutions

Henny Lim
Jan 7, 2016

Rule of power of nine:

  1. Powered with even number: Unit digit is always 1

  2. Powered with odd number: Unit digit is always 9

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Evan Hong
May 5, 2015

If you only look at the last digit 9^1 last digit is 9 then9^2 last digit is 1 after that 9^3 last digit it 9 again and a pattern starts(9,1,9,1,9,1....). So all the odd digits end with 9 and the evens end with one therefore 101 is odd so it ends with a nine.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Evan Hong's good explanation of Henny Lim's simple solution.

J B - 2 years, 10 months ago
Laurent Shorts
Apr 12, 2016

Modulus 10, 9 101 ≡ ( − 1 ) 101 = − 1 ≡ 9 9^{101}\equiv (-1)^{101} = -1 \equiv \boxed{9} .

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Md Hasib
May 22, 2015

''9*101 '' this is how i did this

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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