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find the remainder (32)^33^34 when divided by 11?
Read Solution (Total 8)
-
- 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. - 10 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)
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