Problem 71 Evaluate. $$ (-5)^{2} $$... [FREE SOLUTION]

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Chapter 10: Problem 71

Evaluate. $$ (-5)^{2} $$

Short Answer

Expert verified

The value of $(-5)^2$ is 25.

Step by step solution

Understand the Problem

We need to evaluate the expression $(-5)^2$. This means multiplying -5 by itself.

Apply the Exponent to the Base

The expression $(-5)^2$ implies $(-5) \times (-5)$.

Multiply the Numbers

Compute the product of -5 and -5: $(-5) \times (-5) = 25$.Multiplying two negative numbers results in a positive number.

Write the Result

The result of $(-5)^2$ is 25.

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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 that are less than zero. They are represented with a minus sign (-) in front of the number. When dealing with negative numbers, particularly with integer exponents, the rules for multiplication become important.

A single negative number indicates a point below zero on the number line.
In mathematics, two negatives make a positive, particularly when they interact during multiplication.

Understanding how negative numbers interact with each other, especially when raised to a power, is crucial for problems involving exponents.

Multiplication

Multiplication is an arithmetic operation used to calculate the total of one number added to itself a specified number of times. In cases where a number is raised to a power, such as in $(-5)^2$, it signifies multiplying the base number repeatedly.

To multiply whole numbers, consider how multiplication summarises addition:

For example, $-5\times -5$ means adding \-5\times 1 (or \-5) to itself one more time (making it two times).
Negative times negative yields a positive result: $-5\times -5 = 25$.

Multiplication with negative numbers follows specific rules, which change sign outcomes, making it important to clearly understand how these operations affect the product.

Squared Terms

A squared term refers to a number multiplied by itself, denoted mathematically as a number raised to the exponent of 2. For example, $-5^{2}$ indicates $-5\times -5$.

Key aspects of squared terms include:

Squaring a negative number ( ext{(-5)^2}) results in a positive product, since the two negatives cancel each other out.
Squaring simplifies to multiplication of the base number by itself.
It's important to recognize the parentheses around negative numbers, which dictate that the entire negative number should be squared, unlike \-5^{2}\ which would imply only the 5 is squared and then negated.

Being able to recognize and properly handle squared terms will ensure correct calculations involving exponential expressions.

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91影视

Evaluate. $$ (-5)^{2} $$

Short Answer

Step by step solution

Understand the Problem

Apply the Exponent to the Base

Multiply the Numbers

Write the Result

Key Concepts

Negative Numbers

Multiplication

Squared Terms

One App. One Place for Learning.

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