Expert answers to "The value of the operation [9]7 in Z7..."

High School
Geometry
High school geometry
Circles

lwfrgin

Answered question

2021-02-19

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

Answer & Explanation

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 $x = y (\mod m)$ . This relation is called as congruence modulo m.
Calculation:
It is known that, [x] = [y] if $[x = y (\mod m)]$ .
Consider the values and congruence classes modulo m,
${[9]}^{7}$ and m = 7.
It is evident that. Since $9 = 2 (\mod 7)$ . Therefore,
[9]=[2]
${[9]}^{7} = {[2]}^{7}$
$= [2^{7}]$
=[128]
Since 128 = [2] in $Z_{7}$ . Thus ${[9]}^{7} = [2]$ in $Z_{7}$ .
Therefore, the value of the expression is [2].

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