/*! 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 72 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 72

Simplify each expression. $$ (-9)^{2} $$

Short Answer

Expert verified
The result is 81.

Step by step solution

01

Understand the Expression

The expression \((-9)^{2}\)means that the number \(-9\) is raised to the power of 2, or squared.
02

Apply the Squaring Rule

To square a number means to multiply the number by itself. For the expression \((-9)^{2}\),we calculate \((-9) \times (-9) \).
03

Multiply the Numbers

Now perform the multiplication: \((-9) \times (-9) = 81\).Multiplying two negative numbers results in a positive product.

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Key Concepts

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

Squaring
Squaring is a fundamental operation in mathematics where you multiply a number by itself. It鈥檚 like adding a dimension to the original number or seeing how much area a certain length would cover if both sides were equal. Anything raised to the second power is squared.
When you square a number, follow this simple process:
  • Take the original number.
  • Multiply it by itself.
For example, if you have the expression \((-9)^2\), it involves \(-9\) times \(-9\). This means squaring involves calculative symmetry about the origin, creating a seamless doubling effect that's essential in numerous practical applications like finding areas and understanding parabolic paths in physics.
Negative Numbers
Negative numbers can be a bit tricky, especially when involved in operations like squaring. A negative number is any number less than zero, commonly indicated by a minus sign \((-\)).
This sign drastically changes how it behaves in arithmetic operations.
  • When you multiply two negative numbers, the negatives cancel each other out, leading to a positive result.
  • This is because a negative action reversed twice becomes a positive action.
Understanding how negative numbers work, especially when squared, is crucial. For instance, when you take \(-9\) and square it, \((-9)^2=81\) shows that the negatives turn into a positive product. Raising a negative number to an even power always results in a positive outcome.
Multiplication
Multiplication is a shortcut for addition. It tells you how many times to add a number to itself. Multiplication becomes intuitive when you relate it to repeated addition. For instance, \(3 \times 4\) means adding \(3+3+3+3\).
When multiplying, it's important to pay attention to the signs of the numbers involved, as they affect the result:
  • Positive \(\times\) Positive = Positive: \(2 \times 2 = 4\).
  • Negative \(\times\) Negative = Positive: \(-9 \times -9 = 81\), as we saw earlier.
  • Positive \(\times\) Negative = Negative: \(3 \times -2 = -6\).
Recognizing these patterns makes multiplying more straightforward. Multiplication involving negative numbers is especially important as it appears in many areas, including solving algebraic expressions and calculating distances when directions change.

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Most popular questions from this chapter

Fill in the boxes so that each statement is true. (More than one answer may be possible for these exercises.) $$ 7^{\square}=\frac{1}{49} $$

Multiply. $$ 10 x^{2}\left(20 x y^{2}\right) $$

Subtract using a vertical format. $$ \begin{array}{r} 4 z^{2}-8 z+3 \\ -\left(6 z^{2}+8 z-3\right) \\ \hline \end{array} $$

Subtract \(\left(4 y^{2}-6 y-3\right)\) from the sum of \(\left(8 y^{2}+7\right)\) and \((6 y+9)\)

Subtract \(\left(3 x^{2}-4\right)\) from the sum of \(\left(x^{2}-9 x+2\right)\) and \(\left(2 x^{2}-6 x+1\right)\)
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