Simplify. (-3^3-2 ·3^2)/(8 ÷2^2-(6-|2-15|))

Name: Problem 55, Chapter 1: Elementary and Intermediate Algebra
Uploaded: 2020-06-04T19:51:55-08:00
Duration: 4 min 43 s
Channel: Naomi Motes
Description: Simplify. (-3^3-2 ·3^2)/(8 ÷2^2-(6-|2-15|))

Key Concepts

Order of Operations

This concept governs the sequence in which operations are performed in an expression. It ensures that calculations such as exponentiation, multiplication, division, addition, and subtraction are executed in the correct order to avoid ambiguity in expressions.

Exponents

Exponents denote repeated multiplication of a base by itself. Mastering exponents is essential for simplifying expressions, as they require careful handling during operations such as multiplication and division, especially when negative signs or coefficients are involved.

Absolute Value

The absolute value of a number represents its distance from zero on the number line, disregarding its sign. This concept is critical in expressions that include nested operations, as it introduces a non-linear element that must be resolved before performing further arithmetic operations.

Fraction Simplification

Simplifying a fraction involves reducing it by performing distinct arithmetic operations on the numerator and denominator before combining them. This often requires applying the order of operations carefully to both parts of the fraction to obtain a simplified result.

Transcript

00:01 All right.

00:03 So we have a question where we need to solve or to simplify.

00:09 When you have this division bar that's right here and it covers everything but separating the numerator and denominator, what is going on is that there are these invisible parentheses or brackets that go around the numerator and the denominator.

00:31 Stating that the numerator and denominator need to be simplified and solved first before you can divide.

00:42 So a lot of people get confused.

00:45 They see this division sign.

00:47 They want to do parentheses, then exponents, and then divide across numerator and denominator.

00:55 But because it is reaching that entire numerator and that entire denominator, that needs to happen first before division can happen.

01:04 So once i do that, i went ahead and made it my invisible, parentheses visible, and then i basically just have two different questions.

01:15 So i'm going to solve these separately.

01:18 I'm going to separate the numerator and denominator and solve them separately.

01:22 So first, i'm going to solve the numerator.

01:26 I see that i don't have any parentheses.

01:29 However, i do have exponents.

01:31 Negative 3 to the 3.

01:33 So 3 to the 3 power is 27, and it's going to be a negative 27.

01:40 Rewrite minus 2 because i'm not there yet.

01:43 And then multiply by 3 to the second.

01:45 That's 3 times 3, which is 9.

01:48 I'm going to do 2 times 9, which is 18, because that is my next step.

01:56 After i'm done with my exponents, i have multiplication.

02:02 Rewrite everything else exactly the way that it's supposed to be, and then do the rest of this math.

02:10 So this is basic integer rule.

02:13 I don't have addition, but i did have subtraction, but i did change it with my keep change change rule, and this is going to be a negative 45, right? so i've simplified the numerator, so i'm going to go ahead and put it there.

02:30 All right, and then i'm going to do that same thing with the denominator.

02:34 I'm separating these two completely because they need to be solved first before i can divide.

02:43 All right.

02:48 So parentheses or any type of brackets, absolute value brackets are considered a bracket.

02:54 So i need to do that first.

02:56 All right, because i look inside my parentheses...

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