what is the remainder of (128)^1000 %9 ?

• (128)^1000/9=(126+2)^1000
  ==>(2^3)^111 *2
  ==>(9-1)^111 *2
  ==> -(1)^111 *2
  ==>-2
  so 7 is the remainder
  
• 11 years agoHelpfull: Yes(22) No(6)
• 128^1000/9 = 2^1000/9 = (8)^333*2/9= 8*2/9 = 16/9 = 7 will be the remainder. tats it.
  
• 11 years agoHelpfull: Yes(10) No(0)
• Guys..pls check this site...
  http://www.pagalguy.com/news/cat-2012-quantitative-aptitude-cyclicity-remainders-a-8795869
  the cyclicity of remainders when 128^n is divided by 9 is=>(2,4,8,77,5,1) i.e 6
  1000/6 gives remainder 4
  from the cyclicity list,the remainder is the no. 4 term i.e 7
  easy na???
• 11 years agoHelpfull: Yes(9) No(0)
• (128)^1000%9=(2^3)^333*2%9
  (8)^333*2 %9
  (-1)333*2 %9
  -1*2%9
  -2%9=-2.....==7
  
  ==
• 11 years agoHelpfull: Yes(6) No(2)
• no one xplained clearly....
• 10 years agoHelpfull: Yes(5) No(0)
• ans 7
  (9*14+2)^1000/9
  =2^1000/9 (remainder theorem)
  =(2^3)^333.2/9
  =(9-1)^333.2/9
  =-1.2/9
  =-2/9
  =7
• 11 years agoHelpfull: Yes(3) No(0)
• 7
• 11 years agoHelpfull: Yes(1) No(1)
• 128^1000=2^7000
  Apply Fermit's Theorem i.e.
  2^3=-1(mod9)
  (2^3)^2333=(-1)^2333(mod9)
  2^6999*2=-1*2(mod9)
  2^7000=-2(mod9)
  so the remainder is -2
  
• 10 years agoHelpfull: Yes(1) No(0)
• 128^1000 % 9
  
  (126+2)^1000
  
  2^1000 = (8^333)*2= (-1)^333*2 = -2%9=7
  
  7 is the req. ans as simple as that....
  :-}
  
  
  
  
  
  
• 10 years agoHelpfull: Yes(1) No(1)
• 128^1000 can also be written as 2^7000 and i am spitting 2^7000 as 2^6999*2 and 2^6999=8^2333 so 8^2333*2/9 is equal to -1^2333*2 so remainder is -2 and when prompted we get 9-2 7 as remainder
• 10 years agoHelpfull: Yes(1) No(0)
• (64*2)^1000/9
  remainder depends upon 2^1000/9 = (((2^6)^166)*2^4)/9
  now the remainder depends upon (2^4)/9 = 7
• 11 years agoHelpfull: Yes(0) No(2)
• Remainder 2
  As 128 by dividing 9 leaves remainder 2 So
  2^1000 divided by 9 leaves remainder 2.
• 11 years agoHelpfull: Yes(0) No(4)
• 7 will be the answer !!!
• 11 years agoHelpfull: Yes(0) No(0)
• 7(by remainder theorem)
  
• 11 years agoHelpfull: Yes(0) No(0)
• 7 is the remainder
• 11 years agoHelpfull: Yes(0) No(0)
• 7 is the answr....
• 11 years agoHelpfull: Yes(0) No(0)
• please xplain clearly
  
• 11 years agoHelpfull: Yes(0) No(0)
• its 49
  the 16 year is calculated on the four peaple.just because of every peaple cross 4 year according to thier ages,so avg age=(45*4+16+49)/5=49
• 11 years agoHelpfull: Yes(0) No(6)
• (128)^1000/9=2^1000/9=(2^6)^166/9 * 2^4/9=2^4/9=7
  so remainder=7
• 11 years agoHelpfull: Yes(0) No(0)
• Ans=0
  128^1000 stands for 128 XOR 1000= 720
  720%9=0
• 10 years agoHelpfull: Yes(0) No(1)
• 128%9=2
  so we have to found 2^1000 %9
  now 2^3 %9=-1
  so 2^1000 %9 = (2^999)2%9 = ((2^3)^333)2%9=((-1)^333)2%9= (-2)%9=7
  so ans=7
• 10 years agoHelpfull: Yes(0) No(0)
• any one please explain it clearly.........
• 9 years agoHelpfull: Yes(0) No(0)
• Abe Bah#n Ch%do agar ans short may likhna ha to eha pay maat likhoo...lerkibazi karne ka jaga nehii hain . focusii kar ra ha or idhar dimak garam ho raha hay.
• 9 years agoHelpfull: Yes(0) No(0)