Problem 75 Simplify the given expression. ... [FREE SOLUTION]

91影视

Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 5: Problem 75

Simplify the given expression. $6.3-4.2(9.3)^{2}$

Short Answer

Expert verified

The simplified expression is -356.958.

Step by step solution

Evaluate the Exponent

Calculate the square of 9.3. $ (9.3)^2 = 9.3 \times 9.3 = 86.49 $

Multiply by 4.2

Multiply the result from Step 1 by 4.2. $ 4.2 \times 86.49 = 363.258 $

Subtract from 6.3

Subtract the result from Step 2 from 6.3. $ 6.3 - 363.258 = -356.958 $

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Order of Operations

When simplifying mathematical expressions, it is crucial to follow the correct order of operations known as PEMDAS. This acronym stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Each type of operation is performed in a specific sequence to ensure that the expression is simplified correctly.

Start with operations inside Parentheses.
Evaluate Exponents.
Perform Multiplication and Division from left to right.
Finally, do Addition and Subtraction from left to right.

In the given expression $6.3-4.2(9.3)^{2}$, following the order of operations ensures accurate results. The exponent is solved first, followed by multiplication, and finally subtraction.

Performing Arithmetic Operations

Arithmetic operations form the basis of many mathematical problems and include addition, subtraction, multiplication, and division. When simplifying expressions, knowing when to perform each operation is crucial.

In the present exercise, we encounter different operations:

Multiplication: We see this in 4.2 multiplied by the result of $(9.3)^2$.
Subtraction: This is applied when we subtract the product of 4.2 and $(9.3)^2$ from 6.3.

By adhering closely to the order of operations, you can accurately carry out these operations step-by-step without confusion.

Working with Exponents

Exponents are a key part of mathematical calculations that represent the number of times a number is multiplied by itself. For instance, the expression $(9.3)^2$ means 9.3 is multiplied by itself once. It is like saying "9.3 squared."

Calculate exponents first when simplifying expressions after handling parentheses.
In the expression $(9.3)^2$, you'll calculate it as 9.3 times 9.3, giving the result of 86.49 as shown in the solution steps.

Understanding exponents is vital because they can significantly affect the outcome of an expression. Handle them carefully and early on in the order of operations to simplify complex expressions accurately.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify the given expression. \(6.3-4.2(9.3)^{2}\)

Short Answer

Step by step solution

Evaluate the Exponent

Multiply by 4.2

Subtract from 6.3

Key Concepts

Understanding the Order of Operations

Performing Arithmetic Operations

Working with Exponents

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Pure Maths

Probability and Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.