Problem 101 Perform the indicated operation.... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 2: Problem 101

Perform the indicated operation. $$(-7)^{2}$$

Short Answer

Expert verified

The result is $49$.

Step by step solution

- Understand the Problem

You are given the expression $(-7)^2$ and need to simplify it by performing the indicated operation.

- Recall Squaring a Number

Remember that squaring a number means multiplying the number by itself. In general, for any number $a$, $a^2 = a \cdot a$.

- Apply the Squaring Operation

Apply the squaring operation to $-7$. Write: $(-7) \cdot (-7)$.

- Multiply the Numbers

Multiply $-7$ by $-7$. $-7 \cdot -7 = 49$.

- Write the Final Answer

The result of $(-7)^2$ is $49$.

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Key Concepts

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

exponents

Exponents are mathematical notations indicating the number of times a number, called the base, is multiplied by itself. For example, in $(-7)^2$, $2$ is the exponent and $-7$ is the base. Exponents are written as superscript numbers to the right of the base. The expression $a^n$ indicates that $a$ is multiplied by itself $n$ times. This includes:
$\begin{align*} a^2 &= a \times a, \ a^3 &= a \times a \times a, \ a^4 &= a \times a \times a \times a \ \text{and so on.} \end{align*}$
In the given problem, $a = -7 \text{ and } n = 2.$ So, $ (-7)^2 = -7 \times -7 $.

negative numbers

Negative numbers are numbers less than zero and are represented with a minus sign (-). In arithmetic operations involving negative numbers, several key rules must be remembered:

Multiplying two negative numbers results in a positive number. For example, $ -7 \times -7 = 49 $.
Adding two negative numbers gives a more negative number. For example, $ -3 + -4 = -7 $.
Subtracting a negative number is the same as adding its positive. For example, $ -5 - (-2) = -5 + 2 = -3 $.

In our exercise, we see this in action when multiplying $ -7 \times -7$, resulting in $49$.

multiplication

Multiplication is one of the basic arithmetic operations that combines two numbers to form a product. It can be thought of as repeated addition. For example, $ 3 \times 4 $ can be understood as adding $3$ four times: $ 3 + 3 + 3 + 3 = 12 $. Some important properties of multiplication include:

Commutative Property: $ a \times b = b \times a $
Associative Property: $ (a \times b) \times c = a \times (b \times c) $
Distributive Property: $ a \times (b + c) = a \times b + a \times c $

In our context, the multiplication of $-7 \times -7$ results in the product $49$, demonstrating the rule that the product of two negative numbers is positive.

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91影视

Perform the indicated operation. $$(-7)^{2}$$

Short Answer

Step by step solution

- Understand the Problem

- Recall Squaring a Number

- Apply the Squaring Operation

- Multiply the Numbers

- Write the Final Answer

Key Concepts

exponents

negative numbers

multiplication

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