Simplify. ((-2)^3+4^2)/(3-5^2+3 ·6)

Name: Problem 53, Chapter 1: Elementary and Intermediate Algebra
Uploaded: 2020-06-03T22:13:05-08:00
Duration: 5 min 49 s
Channel: Naomi Motes
Description: Simplify. ((-2)^3+4^2)/(3-5^2+3 ·6)

Key Concepts

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. Mastery of these basic operations is fundamental for simplifying and evaluating expressions. The correct application of these operations, in accordance with the order of operations, is necessary for accurate computation.

Simplification

Simplification is the process of reducing an expression to its simplest form by carrying out all possible operations and combining like terms. This involves following the order of operations, accurately handling exponents and other arithmetic operations, and reducing the expression to a form that is more easily interpreted or solved.

Order of Operations

This concept refers to the rules that dictate the sequence in which the operations in a mathematical expression should be performed. Typically remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), it ensures that expressions are evaluated consistently and correctly.

Exponents

Exponents represent repeated multiplication of a number by itself, and they are evaluated immediately after handling any expressions inside parentheses. They play a crucial role in simplifying expressions, and understanding their properties is essential for accurately computing values, especially when negative bases are involved.

Transcript

00:01 All right.

00:02 So another expression to simplify and solve.

00:06 When you have a fraction problem, yes, this is a fraction problem.

00:13 I want you to take one big deep breath because it's going to be okay.

00:19 Okay? these are very simple.

00:21 If you just stop and think about your order of operations and just take it one step at a time, that's all you've got to do.

00:30 All right so come on all right one big thing that you need to know when you have a division problem there's multiple steps going on in the numerator multiple steps going on in the denominator and that fraction bar covers everything okay what you need to know and just need to remember is that what that's telling you is that the numerator and denominator need to be simplified and and solve to be one number before that division can happen.

01:19 So this division is going to be the last thing that you do because these are in what i like to call invisible math.

01:29 They're in invisible parentheses.

01:31 So i have made my parentheses, which i mean them brackets, but brackets and parentheses kind of go hand in hand, to make it visible and a little more understandable.

01:43 So i'm just going to take it one step at a time.

01:47 I'm going to start with my numerator.

01:49 So i have negative 2 to the third power plus 4 to the second.

01:54 All right.

01:55 So i don't have any parentheses.

01:57 Well, i do, but it's only one number that is contained in those parentheses.

02:02 So there's nothing i can simplify inside those parentheses.

02:05 So i can skip that.

02:06 I do have exponents.

02:08 I have negative 2 to the third power.

02:11 So i'm going to write that out.

02:14 As negative 2 times negative 2 times negative 2.

02:20 Negative 2 times negative 2 is 4 times negative 2 is going to give you negative 8.

02:29 And then i'm going to rewrite everything else exactly the way that it is.

02:35 So i don't miss anything.

02:37 I don't get confused.

02:51 I'm still going to continue to focus on my numerator that i have.

02:56 I'm just going to take it one step at a time.

02:58 If you can do more than one step at a time, go for it.

03:01 More power to you.

03:04 I'm just kind of trying to take it slow for those of you that are a little harder of understanding.

03:10 So i still have an exponent four to the second, which is going to give me 16, keeping everything else exactly the same, so i don't get it wrong...

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