what is the unit digit of(2^3)^123456
a)2
b)4
c)8
d)6

• (2^3)^123456=2^370368
  Take unit position of power
  2^8=256
  so unit position is 6
  Ans:d)6
• 7 years agoHelpfull: Yes(10) No(3)
• 2^3 = 8
  8^123456= 123456%4=0
  8^4=6(unit digit)
  so answer will be d)6
• 7 years agoHelpfull: Yes(6) No(3)
• ans is 6 because 8^123456 power is divisible by 4 and the remainder is 0 when the remainder is 0 we have to give the power 4 and the unit digit 6
• 7 years agoHelpfull: Yes(2) No(2)
• 2 power 3=8
  find cyclisity of 8 which is 4
  because
  8 power 1=8
  8 power 2=64
  8 power 3 =512
  8 power 4=4096
  8 power 5 =32768
  here observe the unit digit of the answers.8 repeat after 4 cycle.hence cyclicity is 4
  now divide the power i.e 123456 with cyclicity if remainder zero then answer is unit digit of a given power.if remainder is any number then take that number as a power of given number i.e here it is 8.and then take a unit digit of that answer.
• 5 years agoHelpfull: Yes(2) No(1)
• 6
  3*123456=370368
  i.e 2^370368
  370368/4---rem is 0
  so (2)^4
  hence unit digit is 6
• 4 years agoHelpfull: Yes(1) No(0)
• (2^3^)^123456=2^3*123456=2^370368
  2 cycle size=4
  so,370368/4=remainder(0)
  2 unit values=2,4,8,6=so,ans is 6
  
• 7 years agoHelpfull: Yes(0) No(0)
• Guys this is only for finding last digit or unit digit. 2^1=2;2^2=4;2^3=8;2^4-6 so last digit is any either of (2,4,8,6) so repeat counting like 2^5=2 which similar to 2^1 and so on... (hence we multiply the powers i.e; 123456*3=8) so 2^8=2^4=6
• 7 years agoHelpfull: Yes(0) No(0)
• 2^3=8 and units digit in 8^4=6 so (2^3)^123456 is 8^(4×30864) which has units digit=6
• 7 years agoHelpfull: Yes(0) No(0)
• c as 6*8=48
• 7 years agoHelpfull: Yes(0) No(0)
• CONDITION:Divide the index by 4....when the remainder is zero and the base value is even number,then the unit digit is six
  ANSWER:Here the remainder is zero when 123456 is divided by 4 and the base value is even.i.e.. 6(2^3),so the unit digit is 6
• 6 years agoHelpfull: Yes(0) No(1)