The value of the operation [11]^{9} in Z_{12} and to write the answer in the form [r] with 0\leq r<m.

ediculeN

ediculeN

Answered question

2021-03-22

The value of the operation [11]9 in Z12 and to write the answer in the form [r] with 0r<m.

Answer & Explanation

Leonard Stokes

Leonard Stokes

Skilled2021-03-24Added 98 answers

Definition used:
Congruence.
Let m be an integer greater than 1. If xand yare integers, then x is congruent to y modulo m if x — y is divisible by m. It can be represented as x=y±odm. This relation is called as congruence modulo m.
Calculation:
Consider the values and congruence classes modulo m,
[11]9 and m = 12.
It is evident that[x]=[y] if [x=y ±odm]. Since 11=1±od{12}.
Then,
[11]=[-1]
[11]9=[1]9
=[(1)9]
=[-1]
Thus, [11]9=[1] in Z11.
Therefore, the value of the expression is [-1].

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