# Absolute Values - Properties and Rules

in MES Science2 months ago

A while ago, I did a video introducing absolute values and what they were but I did not go through some very useful properties and rules of absolute values. In this video I go over these properties and show, for example, that sqrt(a2) = absolute value of a. I go over some other useful properties so make sure you watch the video!

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# Absolute Values: Properties

## Properties

(1). √(a2) = |a|
(2). |ab| = |a||b|
(3). |a/b| = |a|/|b| where b ≠ 0
(4). |an| = |a|n

For the following rules, suppose a > 0, then:

(5). |x| = a if and only if x = ± a
(6). |x| < a if and only if – a < x < a
(7). |x| > a if and only if x > a or x < – a

### Rule 3

Same as Rule 2 because division can be changed into multiplication:

Let c = 1/b where b ≠ 0.

|a/b| = |ac| and this then follows the same procedure as Rule 2.

### Rule 4

(-a)n and (+a)n can only differ in sign but have the same absolute value: ±|a|n.

Thus, |a|n just means that the result is positive, n-power doesn't affect the sign, thus it is equal to |an|.

### Rules 5, 6, 7

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2 months ago (edited)

Math is not my strong point but I went ahead and watched the video. You're a great teacher and you lay it all out perfectly. The way my mind works it's kind of more right brain and imaginative. I feel things out. So as you started explaining everything and because you were explaining it so well I started daydreaming about multiple universes and fixed point in time and how they are relative 2 different supposed realities.

I kind of got lost in that thought and then I realized oh yeah I'm thinking this way because of a TV show. Sliders. This triggered all these memories from that professor and those math formulas in the first episode. Far out.

I feel confident if I watch this video a few more times while not being in the middle of doing various things I could totally grasp this no problem because you are amazing as a teacher!

I look forward to more videos!

Your content has been voted as a part of Encouragement program. Keep up the good work!

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