units digit in expansion os 2 raised to 51 is:

• ANS :: 8
  
  
  2^1 = 2
  2^2 = 4
  2^3 = 8
  2^4 = 16
  2^5 = 32
  2^6 = 64
  2^7 = 128
  2^8 = 256
  ....
  last digits are {2,4,8,6...,2,4,8,6} i.e.,for every 4 sets the last digits are repeated so 12*4+3 digits so 2^51 has last digit is "8".
• 11 years agoHelpfull: Yes(61) No(6)
• 51/4 -> remainder is 3 ,2^3 = 8
  therefore unit's place digit is 8
  to find unit's place digit
  2^1 = 2,2^2 = 4,2^3 =8,2^4 =6 and again the cycle repeats i.e 2^5 =2
  This cycle repeats after 4 period therefore the power is divided by 4.
• 11 years agoHelpfull: Yes(18) No(1)
• units digit of 2^1=2;2^2=4;2^3=8;2^4=6;2^5=2 AND THIS REPEATS
  so 2^48=6;2^51 units place is 8
  ans is 8
  
• 11 years agoHelpfull: Yes(14) No(0)
• 51/4 -> remainder is 3 ,2^3 = 8
  therefore unit's place digit is 8
  to find unit's place digit
  2^1 = 2,2^2 = 4,2^3 =8,2^4 =6 and again the cycle repeats i.e 2^5 =2
  This cycle repeats after 4 period therefore the power is divided by 4.
• 11 years agoHelpfull: Yes(5) No(2)
• 2^51=2^48*2^3
  units digit in 2^48 is 6
  ...6*8=....8
• 11 years agoHelpfull: Yes(3) No(0)
• Ans: 8
  2^51=(2^48)x 2^3
  =(2^4)^12x8 = 16^12 x 8
  since 6 to the power of anything gives 6 so the product is 48
  unit digit=8
• 11 years agoHelpfull: Yes(2) No(0)
• 8,
  Related to cycle of 2
  
• 8 years agoHelpfull: Yes(0) No(0)
• 8.
  because
  first we divide 51 by 4 then the reminder is 3
  so 2^3=8
• 7 years agoHelpfull: Yes(0) No(0)
• answer :8
  In order to solve this question, Firstly you have to know the power cycles concept::
  2^1=2(ending digit)
  2^2=4(ending digit)
  2^3=8(ending digit)
  2^4=6(ending digit)
  from next the same cycle repeats for all like 2^5=2(ending digit),2^6=4(ending digit),2^7=8(ending digit),2^8=6(ending digit)...........
  now coming to the solution ,,let us find the ending digit of 2^10:::find 10%4 which gives 2 from above cycle [mod value 1 represents ending digit 2,mod value 2 represents ending digit 4,mod value 3 represents ending digit 8, mod value 0 represents ending digit 6], so answer is 4.
  2^20::20%4=0; mod value 0=6 so answer is 6;
  2^51;;;;;51%4=3 mod value 3=8 ::so answer is 8
• 7 years agoHelpfull: Yes(0) No(0)
• cilicity of 2 is 4,divide the power with the remainder will be 3,
  make the remainder power of 2 ,it gives the unit digit that is 8.
• 7 years agoHelpfull: Yes(0) No(0)
• ans=8
  because for every after 2^4 the last digit is 2
  so 4*12=48 and then remaining 51-43=3
  then 2^3 is 8.
• 6 years agoHelpfull: Yes(0) No(1)
• 2^51=51/4 here 4 is the unit cycle of 2
  remainder is 3
  substitute 3 in 51
  2^3=8
  ans is 8
• 6 years agoHelpfull: Yes(0) No(0)
• unit digit is 8
• 6 years agoHelpfull: Yes(0) No(1)