Check the solution to "The value of the operation [11]8 in Z5..."

High School
Geometry
High school geometry
Congruence

Globokim8

Answered question

2021-04-24

The value of the operation ${[11]}^{8}$ in $Z_{5}$ and to write the answer in the form [r] with $0 \leq m$ .

Answer & Explanation

odgovoreh

Skilled2021-04-26Added 107 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 \pm o d m

. This relation is called as congruence modulo m.
Calculation:
It is known that, [x] = [y] if [

x = y \pm o d m

].
Consider the values and congruence classes modulo m,

{[11]}^{8}

and m = 5.
Since

11 = 1 \pm o d 5

, then
[11]=[1]

{[11]}^{8} = {[1]}^{8}

= [1^{8}]

=[1]
Thus,

{[11]}^{8} = [1]

Z_{5}

.
Therefore, the value of the expression is [1].

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