Problem 53 Simplify. $$(-1)^{2}$$... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 2: Problem 53

Simplify. $$(-1)^{2}$$

Short Answer

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Step by step solution

Identify the Expression

The given expression to simplify is $(-1)^2$.

Apply the Exponent Rule

Recall that raising a number to the power of 2 means multiplying the number by itself. Therefore, $a^2 = a \times a$.

Calculate the Product

Compute $(-1) \times (-1)$. Multiplying two negative numbers results in a positive number: $-1 \times -1 = 1$.

Write the Final Answer

Thus, $(-1)^2 = 1$. The simplified result is 1.

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Key Concepts

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

Simplifying Expressions

Simplifying expressions is an important skill in mathematics. It's all about making an expression as simple as possible or reducing it to its most basic form. For the expression $(-1)^2$, we want to replace it with its simplest equivalent value.
The steps often involved in simplifying expressions are:

Identifying the components of the expression
Applying appropriate rules, like exponent rules
Performing any necessary arithmetic operations

By following these steps, you can turn complex expressions into much easier-to-handle forms.

Multiplication Rules

Multiplication rules are crucial when working with algebraic expressions and numbers. They help us understand how to handle operations involving numbers and variables.
Here are some key points to remember:

When multiplying two positive numbers, the result is positive (e.g., $2 \times 3 = 6$).
When multiplying two negative numbers, the result is also positive (e.g., $(-2) \times (-3) = 6$).
When multiplying a positive and a negative number, the result is negative (e.g., $2 \times (-3) = -6$).

In our specific problem, $(-1)^2$, we multiply $-1$ by itself, which according to the rule of multiplying two negative numbers, gives us a positive result (1).

Negative Numbers

Understanding negative numbers is essential in many areas of mathematics. A negative number is simply a number that is less than zero, which is indicated by a minus sign (-).
When you deal with negative numbers in operations like multiplication and exponentiation, it's helpful to keep the following rules in mind:

Multiplying two negative numbers results in a positive number.
Multiplying a negative number by a positive number results in a negative number.
When you raise a negative number to an even power, the result is positive.
When you raise a negative number to an odd power, the result is negative.

In $(-1)^2$, we raise $-1$ to the power of 2 (an even number), resulting in a positive outcome.

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91影视

Simplify. $$(-1)^{2}$$

Short Answer

Step by step solution

Identify the Expression

Apply the Exponent Rule

Calculate the Product

Write the Final Answer

Key Concepts

Simplifying Expressions

Multiplication Rules

Negative Numbers

One App. One Place for Learning.

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