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Chapter 1: Problem 29

Evaluate. $$-7^{2}$$

Short Answer

Expert verified
The short answer is: \(-7^2 = (-7)(-7) = 49\).

Step by step solution

01

Understanding the problem

We need to evaluate \(-7^2\). The exponent 2 means that we have to multiply the base, which is -7, by itself. So the expression can be rewritten as \((-7)(-7)\).
02

Multiplying the numbers

Now, we can simply multiply the two numbers. When you multiply two negative numbers, the result is positive. So, \((-7)(-7) = 49\) Thus, the value 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.

Negative Numbers
Negative numbers play an important role in mathematics. They are numbers less than zero and are usually expressed with a minus sign, like \(-7\). These numbers are essential for expressing values such as debts and temperatures below zero. In this exercise, \(-7\) is the base. When dealing with negative numbers:
  • Always consider the sign. A mistake in signs can lead to incorrect results.
  • Multiplying or dividing two negative numbers results in a positive number.
  • Multiplying or dividing negative and positive numbers results in a negative number.
Understanding these rules will help solve exercises involving negative numbers without confusion. Always pay attention to how operations affect the signs through each step of your solution, especially when exponents are involved.
Multiplication
Multiplication is a fundamental arithmetic operation, often thought of as repeated addition. In algebra, multiplying variables and numbers can involve negative and positive values, as seen in this problem where you multiply \((-7)\) by itself.To multiply any numbers:
  • Multiply the absolute values or magnitudes of the numbers, ignoring their signs initially.
  • Apply rules of signs: two negatives make a positive, and a negative with a positive makes a negative.
  • Consider the placement of numbers; multiplication is commutative, so the order doesn鈥檛 change the result.
In the problem, the negative number \(-7\) is squared, requiring it to be multiplied by itself. Since both numbers are negative, their product is positive, leading to an answer of 49.
Order of Operations
The order of operations is crucial to evaluate expressions correctly. It is often remembered by the acronym PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In the exercise, you're asked to apply an exponent to \(-7\). Here, the order requires handling the exponent before multiplying. However, due to the lack of parentheses in \(-7^2\), only the 7 is considered for the exponent, not the negative sign. This means:- The expression is effectively evaluated as \-1 \cdot (7^2)\- Ignoring order of operations can lead to mistakes.- It's essential to understand how the positioning of negative signs impacts results.Following the order will ensure that complex problems can be solved accurately without errors.

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Most popular questions from this chapter

Write a mathematical expression for each and simplify. The sum of \(-7\) and 20.

Rewrite each expression using the distributive property. Simplify if possible. $$-7(2-6)$$

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Write a mathematical expression for each and simplify. The quotient of \(-100\) and 4 decreased by the sum of \(-7\) and 2
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