find the remainder (32)^33^34 when divided by 11?

• unit digit of 33^34 = 9 i.e odd no.
  
  (32)^33^34 / 11
  
  = (11*3-1)^(-------9) / 11
  = (-1)^(odd) / 11
  = -1/10
  => rem = -1+11 = 10
  
  
• 10 years agoHelpfull: Yes(34) No(3)
• 10
  Since,
  32%11=-1
  So the question reduces to (-1)^33^34
  => (-1)^(odd) = -1
  hence,
  10 should be the answer.
• 10 years agoHelpfull: Yes(20) No(7)
• but here (-1)^33*34
  (-1) ^ even =1 ans
• 10 years agoHelpfull: Yes(11) No(7)
• x^y^z=x^(y*z)
  so 32^33^34=32^(33*34)=32^1122
  32/11(rem=-1)
  so,-1^1122=1
  1/11 [rem=1] answer
• 10 years agoHelpfull: Yes(7) No(2)
• Ans.(32^9)/11
  10^9/11
  1000/11remaindr is10
• 10 years agoHelpfull: Yes(3) No(2)
• 10 is the ans
  (-1)^33^34 as 33^34 will always give odd value
  so rem=10
  
• 10 years agoHelpfull: Yes(3) No(3)
• we can find the unit place of 33^34 by cyclicity method....
  which is: the unit place of 33 is 3.
  the cyclicity of 3 is 4 as: 3^1= unit place 3
  3^2= unit place 9
  3^3=unit place 7
  3^4= unit place 1
  3^5= unit place 3
  3^6= unit place 9 and so on......
  34 is divided by 4 we get the remainder 2.that is last cycle is upto 32 and next cycle starts from 33,34....
  hence unit place 34 is 9...therefore 33^34 is a odd one...
  32%11= -1.
  (-1)^odd/11
  remainder is -1+11=10.
• 9 years agoHelpfull: Yes(2) No(1)
• ans: 10
  32%11=10 or -1
  now... taking powers..
  33^34 last digit by cyclicity is 3 hence no. is odd no. and since
  (-1)^odd hence reminder will be -1
  or 11-1 = 10
  So. ans = 10
• 10 years agoHelpfull: Yes(1) No(2)