/*! 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 36 Simplify each of the numerical e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 36

Simplify each of the numerical expressions. $$ -4(-1)^{2}-3(2)^{3} $$

Short Answer

Expert verified
The simplified expression is -28.

Step by step solution

01

Calculate the Power of (-1)^2

First, evaluate the exponentiation \((-1)^2\). Since any number raised to an even power results in a positive number, \((-1)^2 = 1\).
02

Calculate the Power of (2)^3

Next, evaluate \(2^3\). This involves multiplying 2 by itself three times: \(2 \times 2 \times 2 = 8\).
03

Substitute Values into the Expression

Replace the powers in the original expression with the results you calculated:-4 \((-1)^{2}\) - 3 \((2)^{3}\) becomes -4 \(\times 1\) - 3 \(\times 8\).
04

Evaluate the Multiplications

Now, perform the multiplications: -4 \(\times 1 = -4\) and 3 \(\times 8 = 24\).
05

Simplify the Expression

Combine the results of the multiplications by subtracting: -4 - 24 = -28.

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.

Exponents
Exponents represent the idea of multiplying a number by itself a certain number of times. When you see an expression like
  • \((-1)^2\), read it as "negative one squared." This means \(-1\) is multiplied by itself: \((-1) \times (-1)\).
  • Since multiplying two negative numbers results in a positive number, \((-1)^2 = 1\).
Similarly, for
  • \(2^3\), you're asked to multiply 2 by itself three times: \(2 \times 2 \times 2\). Each successive multiplication helps the number grow rapidly in size.
  • Here, \(2^3 = 8\).
Exponents are powerful tools in math, simplifying repeated multiplication into a neat package.
Order of Operations
When simplifying expressions such as
  • \(-4(-1)^2 - 3(2)^3\), it's essential to follow the order of operations to get the correct answer.
This order, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), dictates the sequence of operations. Given this rule,
  • you calculate the powers first, before tackling multiplications and subtractions.
Following PEMDAS ensures that each step is performed in the proper order, preventing mistakes and helping you reach the correct result.
Negative Numbers
Understanding negative numbers is crucial in mathematics, especially when combined with operations like multiplication.
  • In the expression \(-4(-1)^2 - 3(2)^3\), the negative numbers influence the outcome of arithmetic operations.
  • Multiplying a negative number by a positive number results in a negative product, as seen in \(-4 \times 1 = -4\).
  • Similarly, \(-3 \times 8\) gives -24; thus, the subtraction reflects the negative direction in value.
When combining negative numbers with other operations, carefully track whether you're adding or subtracting to maintain accuracy in the final expression.

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

Evaluate the algebraic expressions for the given values of the variables. $$ 2(x-1)-(x+2)-3(2 x-1), \quad x=-1 $$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. A number subtracted from 75

Answer the question with an algebraic expression. Crystal is \(n\) years old. How old was she 5 years ago?

Simplify the algebraic expressions by removing parentheses and combining similar terms. $$ 4\left(n^{2}+3\right)+\left(n^{2}-7\right) $$

Answer the question with an algebraic expression. Jesse has \(n\) nickels, \(d\) dimes, and \(q\) quarters in his bank. How much money, in cents, does he have in his bank?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.