/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 Determine each of the values. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 37

Determine each of the values. $$ (|4|+|-6|)^{2}-(|-2|)^{3} $$

Short Answer

Expert verified
The value is 92.

Step by step solution

01

Calculate Absolute Values

Begin by evaluating the absolute values in the expression. The absolute value of a number is its distance from zero, ignoring the sign. - \(|4| = 4\) - \(|-6| = 6\) - \(|-2| = 2\)
02

Sum of Absolute Values

Add the absolute values of \(4\) and \(-6\).\(|4| + |-6| = 4 + 6 = 10\)
03

Square the Sum

Square the result from Step 2.\((|4| + |-6|)^2 = 10^2 = 100\)
04

Cube the Absolute Value of -2

Calculate the cube of the absolute value of \(-2\).\((|-2|)^3 = 2^3 = 8\)
05

Subtract the Cubed Value from the Squared Value

Subtract the result from Step 4 from the result from Step 3.\((|4| + |-6|)^2 - (|-2|)^3 = 100 - 8 = 92\)

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 Absolute Value
Absolute value is a fundamental concept in mathematics, and it's all about understanding the distance of a number from zero on the number line, regardless of direction. Absolute value turns any negative number into a positive number. Consider these points when working with absolute values:
  • Symbol: The absolute value of a number \( x \) is written as \(|x|\).
  • Basic Rule: \(|x|\) is the same as \(x\) if \(x \geq 0\), and it is \(-x\) if \(x < 0\).
  • Example: For the number \(-6\), the absolute value \(|-6|\) is \(6\) because it's the distance from zero.
Understanding this concept is crucial as it forms the first step in solving expressions like the one given.
Mastering Order of Operations
The order of operations is a set of rules that dictates the sequence in which operations are carried out. This is essential for consistent results in mathematics. Remember the acronym PEMDAS:
  • **P**arentheses
  • **E**xponents (including powers and roots)
  • **MD** (Multiplication and Division, from left to right)
  • **AS** (Addition and Subtraction, from left to right)
In the exercise, after computing the absolute values, the operations follow with exponentiation (squaring and cubing) before subtraction. Ensuring the correct order is followed prevents mistakes and the wrong answer.
Squaring Numbers
Squaring a number involves multiplying the number by itself. Here are some important points about squaring:
  • Squaring a number \( x \) is written as \(x^2\).
  • The result of a square is always positive since a negative number squared turns positive. For example, \((-5)^2 = 25\).
  • In our exercise, \((|4| + |-6|)^2 = 10^2 = 100\).
Understanding how squaring works help simplify expressions and equations in various mathematical problems effectively.
Exploring Cubing Numbers
Cubing a number means raising it to the third power, which involves multiplying the number by itself three times. Here鈥檚 how to think about cubing:
  • Cubing a number \( x \) is denoted as \(x^3\).
  • A cube retains the sign of the original number鈥攏egative numbers remain negative and positive numbers remain positive. For example, \((-3)^3 = -27\).
  • In the given example, \((|-2|)^3 = 2^3 = 8\).
Cubing is an exponential operation that is crucial in various contexts, including volume calculations and transformations in geometry.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Determine each value. $$ -(-|-16|) $$

Find the value of each of the following. Use a calculator to check each result. $$ 6(-2-9)-6(2+9)+4(-1-1) $$

How many units are there between the given pair of numbers? 0 and 4

For the following 4 problems, perform the indica ted operations $$ -0.012-(-0.111)-(0.035) $$

How should each number be read? $$ -8 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.