The value of the operation [9]^{7} in Z_{7} and to write the answer in the form [r] with 0 \leq r < m.

lwfrgin

lwfrgin

Answered question

2021-02-19

The value of the operation [9]7 in Z7 and to write the answer in the form [r] with 0r<m.

Answer & Explanation

Nathaniel Kramer

Nathaniel Kramer

Skilled2021-02-21Added 78 answers

Definition used:
Congruence.
Let m be an integer greater than 1. If x and y are integers, then x is congruent to y modulo m if x — y is divisible by m. It can be represented as x=y(modm). This relation is called as congruence modulo m.
Calculation:
It is known that, [x] = [y] if [x=y(modm)].
Consider the values and congruence classes modulo m,
[9]7 and m = 7.
It is evident that. Since 9=2(mod7). Therefore,
[9]=[2]
[9]7=[2]7
=[27]
=[128]
Since 128 = [2] in Z7. Thus [9]7=[2] in Z7.
Therefore, the value of the expression is [2].

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