2988^687,what will be the last 3 digit

• 988=(990-2)^687
  if we subtract last 3 digits of 2^687 from the last 3 digits of 990^687(which will be 000) then we get the last 3 digits of 2988^687
  The last 3 digits of 2^687=8*2^684=8*16^171=8*16^(5*34+1)=16*8 i.e 128, so last 3 digits of 2988^687 is ....0000-128=872
• 11 years agoHelpfull: Yes(33) No(14)
• ans:872
  period of 8 (8,4,2,6,8,4,2,6........) is 4,hence when 687 divide by 4 we will get 3 as remainder
  hence for last 3 digit no we just have to calculate 88^3=(88*88)*88=44*88=872(last 3 digits)
• 11 years agoHelpfull: Yes(15) No(7)
• divide 687 by 4
  then rem will be 3
  so 8^3 is 512
  that is ans.
• 11 years agoHelpfull: Yes(7) No(7)
• 592 must be the answer.
  
• 11 years agoHelpfull: Yes(6) No(4)
• 562 is the answer
• 11 years agoHelpfull: Yes(5) No(11)
• ans is 512
• 11 years agoHelpfull: Yes(3) No(5)
• please explain the procedure....
• 11 years agoHelpfull: Yes(2) No(0)
• Last 3 digit of the expression 2988^687 depends upon last 3 digit of 88^687. So last 3 digit of 88^687= (2*44)^687 -> = 2^687 * 44^687 -> = (2^10)^68 * 2^7 * (44^2)^343 * 44 -> = 76 * 28 * 16 * 44 -> = 1498112 .... So 112 will be the last 3 digit
• 11 years agoHelpfull: Yes(2) No(0)
• 988=(990-2)^687
  if we subtract last 3 digits of 2^687 from the last 3 digits of 990^687(which will be 000) then we get the last 3 digits of 2988^687
• 11 years agoHelpfull: Yes(1) No(1)
• Unit Digit of any no. repeats after power 4n where n=0,1,2.....
  Ex.:-7^1=7
  7^2=9(Unit digit)
  7^3=3(Unit digit)
  7^4=1(Unit digit)
  Unit Digit of 7^5=7 is same as 7^1=7.
  i.e.in this question divide 687 by 4.then rem will be 3 so 8^3=512.
  
• 11 years agoHelpfull: Yes(1) No(4)
• (2^10)^68 * 2^7 * (44^2)^343 * 44
  = 76 * 28 * 16 * 44(last two digits of each expression) = 1498112 ....
• 11 years agoHelpfull: Yes(1) No(1)
• Take last three digits.
  988^1=988
  988^2=144
  988^3=272
  988^4=--6
  last digit repeats for every 4 cycle, 687 % 4= remainder is 3
  so 272 is the ans.
  
• 10 years agoHelpfull: Yes(1) No(0)
• 91 is the answer
• 11 years agoHelpfull: Yes(0) No(12)
• 2888^687
  dividing 687 by 4 gives a remainder 3.
  no 8^3= 512
  so last 3 digits of 2988^687 is 512
• 11 years agoHelpfull: Yes(0) No(13)
• 192
  check your windows calculator
  go by options is what i can suggest
  check last digit ie 2
  then second last digit 88^7=92
  
• 11 years agoHelpfull: Yes(0) No(0)
• Answer is 984
• 11 years agoHelpfull: Yes(0) No(0)