unit's digit in the no' (12357)^655
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(12357)^655
The unit digit of 12357 which is 7 determines the value of the exponent (12357)^655
Therefore we have to find the unit digit of the exponent 7^655 to find the unit digit of (12357)^655
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16,807
Therefore 7 repeats in the unit digit after every forth power of 7 and any exponent in the form 7^4n+1 ends in the unit digit 7
7^655=7^4(163)+1 × 7^2
=7×49=343
unit digit of 343 is 3
Therefore the unit digit of the exponent (12357)^655 is 3
The unit digit of 12357 which is 7 determines the value of the exponent (12357)^655
Therefore we have to find the unit digit of the exponent 7^655 to find the unit digit of (12357)^655
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16,807
Therefore 7 repeats in the unit digit after every forth power of 7 and any exponent in the form 7^4n+1 ends in the unit digit 7
7^655=7^4(163)+1 × 7^2
=7×49=343
unit digit of 343 is 3
Therefore the unit digit of the exponent (12357)^655 is 3
tezzzz30:
your ans is right but you have done a very long procedure for this.
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3
Answer:
Step-by-ste
p(12357)^655
The unit digit of 12357 which is 7 determines the value of the exponent (12357)^655
Therefore we have to find the unit digit of the exponent 7^655 to find the unit digit of (12357)^655
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16,807
Therefore 7 repeats in the unit digit after every forth power of 7 and any exponent in the form 7^4n+1 ends in the unit digit 7
7^655=7^4(163)+1 × 7^2
=7×49=343
unit digit of 343 is 3
Therefore the unit digit of the exponent (12357)^655 is 3
_________________
@phenom
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