Problem 52 Compute the exact value. \((-2... [FREE SOLUTION]

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Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 2: Problem 52

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

Short Answer

Expert verified

The exact value of $(-2)^{2}$ is 4.

Step by step solution

Identify the Problem

We need to compute the exact value of the expression $(-2)^{2}$. This involves squaring the negative number -2.

Apply the Exponent Rule

Recall that squaring a number means multiplying the number by itself. Therefore, $(-2)^{2} = (-2) imes (-2)$.

Perform the Multiplication

Now perform the multiplication of the two numbers. A negative number multiplied by a negative number gives a positive result: $(-2) imes (-2) = 4$.

Conclude the Solution

The exact value of the expression $(-2)^{2}$ is $4$.

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Key Concepts

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

Negative Numbers

Negative numbers are numbers less than zero. They are usually represented with a minus sign (-) in front of them. Understanding negative numbers is important for many mathematical concepts, including subtracting and multiplying. When you multiply or divide two negative numbers, the result is a positive number. However, if you multiply or divide a positive number by a negative number, the result is a negative number.

Example: * -3 is a negative number. * -3 x -3 = 9 (because two negatives make a positive)
Operations with negative numbers follow specific rules that you need to memorize.

Squaring Numbers

Squaring a number means multiplying the number by itself. This operation is represented as raising the number to the power of 2. For example, if we square -2, we write this as (-2)^{2}. It's crucial to note that when a negative number is squared, the result is always positive:

This is because multiplying two negative numbers gives a positive number. * Ex: (-2) x (-2) = 4
Mathematically, the operation is similar for any integer.
Squaring is a form of exponentiation, which is a key concept in algebra.

Multiplying Integers

Multiplying integers involves a straightforward set of rules that makes it easy to predict the sign of the result. Here are the rules to remember:

Positive x Positive = Positive
Negative x Negative = Positive
Positive x Negative = Negative
Negative x Positive = Negative

For instance, with the example of (-2) x (-2), since both integers are negative, they multiply to give a positive result, which is 4. This can often be confusing but remembering that two negatives make a positive can help you solve these problems easily.

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91影视

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

Short Answer

Step by step solution

Identify the Problem

Apply the Exponent Rule

Perform the Multiplication

Conclude the Solution

Key Concepts

Negative Numbers

Squaring Numbers

Multiplying Integers

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