What is the unit’s digit in the number got from the following operation: (23)10
3
9
7
1
8

• unit digit 3 has cyclicity 4
  10/4=remainder is 2
  hence 3^2=9
• 7 years agoHelpfull: Yes(13) No(0)
• first its not ankith its ankit...............apply the process of unit digit finding as it is 23^10.
  now break it in the power of ((23)^4)^2 *23^2
  [ (..3)*(..3)*(..3)*(..3)]^2 *[(..3)*(..3)]
  [(..9)*(..9)]^2 *[..9]
  [(..81)^2]*(..9)
  (..1)^2 *(..9)
  (...1) *(..9)=9
  answer is 9
  
  you can verify by using 23^10 on calculator
• 7 years agoHelpfull: Yes(7) No(0)
• cyclicity of 3 is 4. when we divide 10 by 4, it is 2. 3^2 is 9. So, ans is 9
• 7 years agoHelpfull: Yes(2) No(0)
• 9
  coz 3^0=1, 3^1=3, and this goes on and we get 3^10 as 9(in the unit digit)
• 7 years agoHelpfull: Yes(1) No(0)
• Ans:-3
  The last digit in lower value
• 7 years agoHelpfull: Yes(0) No(3)
• 9 will be the answer
• 7 years agoHelpfull: Yes(0) No(0)
• hi ankith can u explain how it is 9
• 7 years agoHelpfull: Yes(0) No(0)
• 10÷4=remainder =2 now 3^2=9 hence unit digit is 9
• 7 years agoHelpfull: Yes(0) No(0)
• We want to find the unit digit of 23 power 10
  Now
  consider 3 in 23
  
  3*1=3is the unit digit in the same way
  3*3=9
  9*3=7
  7*3=1
  1*3=3(again 3 unit digit repeated)
  so for power 4 we get 3 as unit digit
  They have asked power 10
  so, 10-8=2
  so power 2 gives 9 as the unit digit
• 7 years agoHelpfull: Yes(0) No(0)
• check whether the power value is fourth multiple.... 10 is not a 4th multiple..so take 4th multiple closest to 10.. 8 is a 4th multiple..reminder is 2. then 23^8 * 23^2 . for the power 4th multiple ...if the number is odd number , ans is 1 (is the number's power is 4th multiple). and we know that 9 is a unit digit for 23^2 .. so
  
  23^8 *23^2= > (1)*(9) = 9 is an answer (unit dig)
  
  another examples -
  1) 13^36 = 1 ( 36 is multiple of 4 so 1 is a unit dig if the no is odd , 6 is a unit dig if a no is even )
  2) 56^19 = 56^16 * 56 ^2 = (6) * (6) = 6
• 7 years agoHelpfull: Yes(0) No(2)
• 3^10 =59049 unitdigit is 9
• 7 years agoHelpfull: Yes(0) No(0)