/*! 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 5 \(\mathrm{T} / \mathrm{F}:\) In ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 5

\(\mathrm{T} / \mathrm{F}:\) In the expression \(-2^{2},\) only " \(2 "\) is squared, not \("-2 . "\) Explain.

Short Answer

Expert verified
True, only "2" is squared; the negative sign is applied afterwards.

Step by step solution

01

Understand the Expression

The expression given is \(-2^2\). It's important to recognize that the negative sign is not included in the exponentiation according to standard order of operations. Thus, the expression is evaluated as the negative of \(2^2\).
02

Apply Order of Operations

The order of operations states that we must calculate exponents before applying any other operations, like multiplication or negation. Therefore, solve \(2^2\) first, which equals \(4\).
03

Apply the Negative Sign

Once the exponentiation is resolved, apply the negative sign to the result. So, \(-2^2\) becomes \(-1 \times 4\), which equals \(-4\).
04

Conclusion

In conclusion, only the \(2\) is squared, not the \(-2\). The negative sign is applied after the exponentiation, resulting in \(-4\). It's essential to bracket the negative if you want the entire \(-2\) to be squared, i.e., \((-2)^2\) would equal \(4\).

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.

Exponentiation
Exponentiation is a mathematical operation that involves raising a base number to the power of an exponent. It is a way of expressing repeated multiplication of the base. For instance, in the expression \(2^2\), the number 2 is the base and 2 is the exponent, meaning you multiply 2 by itself once, resulting in 4. Unlike addition or multiplication, exponentiation has a specific placement in the order of operations, making it crucial to address exponents before other operations. This priority ensures calculations are accurate, particularly when negative numbers are involved. Understanding how and when to apply exponentiation according to these rules can save you from common mistakes.
Negative Numbers
Negative numbers are integers less than zero and are represented by a minus sign (-) preceding the number. They can be tricky, especially in operations like exponentiation. When a negative sign appears in front of an exponent, as in the expression \(-2^2\), it is crucial to remember that only the positive base is affected by the exponent, while the negative sign acts as a multiplier afterward. This situation is a common source of confusion but can be addressed by adhering to the order of operations. To raise an entire negative number to a power, parentheses must be used, such as in the expression \((-2)^2\), to ensure the negative sign is included in the exponentiation process. Without parentheses, the negative sign is only applied after raising the base to the power, a distinction that greatly affects the outcome.
Parentheses in Math Expressions
Parentheses play a crucial role in mathematical expressions by altering the order of operations. They signal that the operations contained within them should be performed first, overriding the standard order of operations.In expressions where a negative number needs to be raised to a power, parentheses ensure the negative sign is included in the exponentiation. For example:
  • \((-2)^2\) means both the negative sign and the number 2 are squared, resulting in 4.
  • Without parentheses, such as in \(-2^2\), only the 2 is squared, and the negative sign is applied after, resulting in -4.
Using parentheses correctly can change the result of an expression entirely, and being aware of this can prevent errors.

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 described mathematical statement, or determine how the described changes affect other variables in the statement as appropriate. The capacitance, \(C,\) of a parallel plate capacitor is given by \(C=\frac{k \varepsilon_{0} A}{d}\) where \(d\) is the distance between the plates. If \(k\), \(\varepsilon_{0},\) and \(A\) are held constant while the distance between the plates decreases, does the capacitance increase, decrease, or stay the same?

Let \(f(x)=x^{3}, g(x)=x+4,\) and \(h(x)=\sin (x) .\) Each of exercise \(5-8\) is some combination of \(f(x), g(x),\) and \(h(x) .\) Determine the type of combination and write it using function notation. For example, \(x^{3}+x+4\) is the addition of \(f(x)\) and \(g(x)\) and can be written as \(f(x)+g(x)\). $$ \frac{x^{3}}{\sin (x)} $$

In exercises \(11-17,\) simplify the given term and write your answer without negative exponents. $$ \frac{e^{x^{2}-1}}{e^{x+1}} $$

In exercises \(8-10,\) simplify and write the given term without using radicals. $$ \left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^{2} $$

Solve the given problem for \(x,\) if possible. If a problem cannot be solved, explain why. $$ 5^{x}=0 $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.