/*! 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 53 Compute the exact value. \((-5... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 53

Compute the exact value. \((-5)^{2}\)

Short Answer

Expert verified
The exact value of \((-5)^{2}\) is 25.

Step by step solution

01

Understanding the Problem

The expression \((-5)^{2}\), denotes raising -5 to the power of 2, which means multiplying -5 by itself.
02

Calculating the Result

Since the exponent is 2, we multiply -5 by -5: \[ (-5) \times (-5) = 25 \]The result of multiplying two negative numbers is positive.
03

Verifying the Calculation

Ensure that the operation was done correctly by reconsidering the multiplication. Multiplying \(-5\) by \(-5\), results in a positive 25 because the product of two negative numbers always results in a positive number.

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 Negative Numbers
Negative numbers are values less than zero. They are commonly represented with a minus sign in front of the number, like -5. These numbers are often used in various real-life situations like temperatures below zero or financial debts.

In mathematics, negative numbers are crucial for performing operations like subtraction where the result could go below zero. The key thing to remember is that the negative sign indicates that the number is on the opposite side of zero from the positive numbers.

When you have two negative numbers, such as -5 and -5, multiplying them involves a special rule. We'll explore this rule further when discussing multiplication.
The Multiplication of Negative Numbers
Multiplication is one of the fundamental arithmetic operations that combines two numbers to get a product. To multiply numbers means you add one number to itself as many times as indicated by the other number. Now, when it comes to negative numbers, things become a bit more interesting.

Here's what you need to know about multiplying negative numbers:
  • Multiplying two positive numbers results in a positive product.
  • Multiplying a positive number by a negative number, or vice versa, gives a negative product.
  • Multiplying two negative numbers results in a positive product.
The last rule is particularly interesting. It may seem odd, but think of it this way: when you multiply a negative by a negative, you're essentially inverting the direction twice, bringing you back to a positive result.

For example, \[ (-5) \times (-5) = 25 \] The negative signs cancel out, resulting in a positive 25.
Basic Mathematical Operations and Negative Exponents
Mathematical operations are actions such as addition, subtraction, multiplication, and division. Each operation becomes more complex when involving negative numbers or exponents.

When dealing with exponents, as in \((-5)^2\), you are performing repeated multiplication.
  • The base, -5, indicates the number being multiplied.
  • The exponent, 2, tells you how many times to multiply the base by itself.
  • In this exercise, the task was to compute \((-5) \times (-5)\).
The calculations show that \((-5)^2\) results in 25, illustrating how negative exponents result in a positive outcome due to the doubling effect of reversing a negative sign.
When you come across mathematical expressions that include negative bases and exponents, remember to apply these rules to accurately compute the value.

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

Three more than eight times an unknown number is \(-29\). Find the unknown number.

Solve the given equation for \(\mathrm{x}\). \(7 x+15=-55\)

Solve the given equation for \(\mathrm{x}\). \(-6 x+20=-64\)

The quotient of two integers is 9 . One of the integers is \(-8\). Find the other integer.

Solve the given equation for \(x\). . \(\mathrm{x}+10=17\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.