what is the unit place of 2^(3^3458) ??

• Lets take the power of 3 first...
  3458%4=2 (2 is remainder that is unit place of power of 3)
  so unit digit of 3^3458=3^2 =9
  So whole eqaution can we written as...
  2^9
  Now,For 2^(9) .... 9%4=1(1 is remainder that is unit place of power of 2)
  so unit digit is=2^1 = 2
• 12 years agoHelpfull: Yes(34) No(6)
• we can also take the problem as 2^10374 / 8^3458
  find cyclics for eithr 2 or 8
  in 8's cycle we got the unit digit no. as 8,4,2,6
  noe 3458/4=864 with remainder 2
  so the secnd no. in cycle that is 4 will be the ans :) you can verify the ans using 2's cycle.
• 12 years agoHelpfull: Yes(8) No(7)
• 2^(3^2)=2^9=2 so ans is 2
• 12 years agoHelpfull: Yes(5) No(7)
• answer will be 4.
• 12 years agoHelpfull: Yes(4) No(5)
• 3's cycle is
  (3)^1=3
  3^2=9
  3^3=27
  after it the unit digits will be repeat...for ex-3^4=81(unit digit is 1 )
  so we wil try to find the closest fully divisible no of 3458
  the closest no(3456 which is divisible by 3 ....which means 3^3456 is unit digit is 7)
  cause 3456+2=3458 so remaining two digit of power will 3^2=9.
  so 2^9=512 so...
  ans is 2.....
• 12 years agoHelpfull: Yes(2) No(5)
• @ pooja because the unit place cycle of 3^n repeats itself after 4 times. for instance 3^1=3
  3^2=9
  3^3=7(27 so at units place 7)
  3^4=1(81 so at units place 1)
  3^5=3 Thus the cycle is repeatng now
  
• 12 years agoHelpfull: Yes(1) No(2)
• 3458%4=2
  so unit digit of 3^3458=3^2=9
  now, 2^(....9) here 9%4=1
  so unit digit is=2^1=1
• 12 years agoHelpfull: Yes(0) No(12)
• actually i forget one thing in my last answer......
  
  
  the correct answer is
  
  3's cycle is
  (3)^1=3
  3^2=9
  3^3=27
  3^4=81
  after it the unit digits will be repeat...for ex-3^5=243(unit digit is 3 )
  so we wil try to find the closest fully divisible no of 3458
  the closest no(3456 which is divisible by 4 ....which means 3^3456 is unit digit is 7)
  cause 3456+2=3458 so remaining two digit of power will 3^2=9.
  so 2^9=512 so...
  ans is 2.....
  
  
  
• 12 years agoHelpfull: Yes(0) No(4)
• for 3^3458 at unit place u get 9.
  2^9(unit place) we get 2
  b'coz unit place for 2^ is 2,4,8,6 sequentially
  so by that at2^9 we get 2
  
• 12 years agoHelpfull: Yes(0) No(3)
• MUKESH SINGH RAJPUT @ why u hv done this 3458%4=2 ...??
  why u hv divided it by 4..???
  plzz explain
• 12 years agoHelpfull: Yes(0) No(0)
• just look at the unit digits
  2^3^8=(8)^8=64, 2 to the power 3 is 8 and 8 to the power is 64, thus on taking unit digit 4 will be the answer
• 12 years agoHelpfull: Yes(0) No(0)