Problem 49 Multiply or divide as indicated.... [FREE SOLUTION]

Chapter 2: Problem 49

Multiply or divide as indicated. See Examples 1 through 14. $$ (-7)^{2} $$

Short Answer

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Step by step solution

Identify the Base and Exponent

In the expression $(-7)^{2}$, -7 is the base and 2 is the exponent. The exponent tells us how many times to multiply the base by itself.

Multiply the Base by Itself

Since the exponent is 2, it indicates that we need to multiply the base $-7$ by itself, which is computed as follows: $(-7)\times(-7)$.

Compute the Product

Calculate the product of $-7\times-7$. Since multiplying two negative numbers results in a positive number, the product is $49$.

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Key Concepts

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

Base and Exponent

In the expression $(-7)^2$, the components include the **base** and the **exponent**. The base here is $-7$, which is the number that will be multiplied repeatedly. The exponent is \2\, which indicates the number of times the base is multiplied by itself.
Understanding these components is crucial when working with exponents.

The base is the main factor in the equation.
The exponent shows how many times the base multiplies itself.

For example, $(-7)^2$ means $-7$ is multiplied by itself two times. This concept helps streamline calculations and is a fundamental principle in algebra and higher mathematics.

Negative Numbers Multiplication

When you multiply negative numbers, there are specific rules to follow to determine the sign of the product. For $(-7) \times (-7)$, you are multiplying two negative numbers.

When two negative numbers are multiplied, the product is positive.
This is because the negatives cancel each other out.

Therefore, multiplying $-7 \times -7$ results in the positive product of 49. This rule forms the basis for handling negative numbers in multiplication across different mathematical problems. Understanding it simplifies calculations and minimizes errors.

Product of Numbers

The term **product** refers to the result of multiplying numbers together. In our working example $(-7)^2$, after understanding both base and exponent, and recognizing the multiplication of negative numbers, the next step is calculating the product.
For $-7 \times -7$, you apply the multiplication rule: multiply magnitudes and apply the appropriate sign based on the multiplication rules:

Magnitudes are simply the numbers without regard to their signs; thus, 7 times 7.
The sign rule: negative times negative equals positive, so $7 \times 7 = 49$.

This process led us from the initial expression to conclude that $(-7)^2$ evaluates to a product of 49.

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91影视

Multiply or divide as indicated. See Examples 1 through 14. $$ (-7)^{2} $$

Short Answer

Step by step solution

Identify the Base and Exponent

Multiply the Base by Itself

Compute the Product

Key Concepts

Base and Exponent

Negative Numbers Multiplication

Product of Numbers

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