/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Evaluate each expression. $$(-... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 6

Evaluate each expression. $$(-6)^{2}$$

Short Answer

Expert verified
The value of \( (-6)^{2} \) is 36.

Step by step solution

01

Understand the notation

The notation \( (-6)^{2} \) represents \( -6 \) times \( -6 \).
02

Carry out multiplication

When a negative number is multiplied by another negative number, the result turns out to be a positive number. Therefore, \( -6 \times -6 = 36 \).

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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 less than zero. They are represented with a minus sign (-) in front of them, for example, -1, -5, or -100. When you have a negative sign, it indicates a value is below zero, which is important in various real-life contexts, like temperatures below freezing or debts in accounting.

Understanding how negative numbers work is crucial for arithmetic operations, as they follow specific rules that might differ from positive numbers. When dealing with equations or expressions involving these numbers, knowing these rules helps prevent common mistakes.
Multiplication
Multiplication is one of the four basic arithmetic operations, essentially repeated addition. For example, multiplying 2 by 3 (2 脳 3) means you add 2, three times: 2 + 2 + 2 = 6.

When we deal with multiplying negative numbers, there's an important rule:
  • A negative number times a negative number results in a positive product. This is because two negatives make a positive. For instance, (-6) 脳 (-6) = 36.
  • However, a negative number times a positive number always results in a negative product. For example, (-3) 脳 4 = -12.
  • Similarly, a positive number times a negative number is also negative. For instance, 5 脳 (-2) = -10.

Being comfortable with these rules of multiplication will ease the handling of complex expressions.
Integer Operations
Integer operations involve the basic mathematical tasks of addition, subtraction, multiplication, and division applied to whole numbers, which can be positive, negative, or zero. An integer is any number in the infinite sequence ranging from ...-3, -2, -1, 0, 1, 2, 3,....

When performing operations on integers, it鈥檚 important to remember the rules that dictate how those operations influence the sign and value of the result:
  • Adding integers: The sum of two positive integers or two negative integers keeps the sign. So, 3 + 5 = 8 and (-3) + (-5) = -8.
  • Subtracting integers: To subtract an integer, add its opposite. That's why subtracting a negative number is the same as adding the corresponding positive number, like 6 - (-2) = 6 + 2 = 8.
  • Multiplying and dividing integers: Follow the same positive/negative rules as discussed in multiplication, remembering that the sign depends on the number of negatives in the operation.

Understanding these operations helps simplify expressions properly and achieve accurate mathematical results.

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Most popular questions from this chapter

Perform each division. Assume no division by \(0 .\) $$\frac{x^{3}+27}{x+3}$$

Perform the operations. $$3\left(x y^{2}+y^{2}\right)-2\left(x y^{2}-4 y^{2}+y^{3}\right)+2\left(y^{3}+y^{2}\right)$$

Simplify or solve as appropriate. $$(x-3)^{2}-(x+3)^{2}$$

The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance. For one driver, the stopping distance \(d\) is given by the function \(d=f(v)=0.04 v^{2}+0.9 v,\) where \(v\) is the velocity of the car. Find the stopping distance when the driver is traveling at \(30 \mathrm{mph}\).

Perform the operation. Subtract \((-4 a+b)\) from \(\left(6 a^{2}+5 a-b\right)\)
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