/*! 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 18 Simplify each expression using t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 18

Simplify each expression using the products to-powers rule. $$(-6 x)^{2}$$

Short Answer

Expert verified
The simplified expression is \(36x^2\).

Step by step solution

01

Apply the Power Rule

First, apply the power rule to \((-6x)^2\). This means both -6 and x are each raised to the power of 2, which results in \((-6)^2 * x^2\).
02

Calculate the Square of -6

Next, calculate the square of -6. The square of a number is the result when that number is multiplied by itself. So, \((-6)^2 = 36\).
03

Write the Final Expression

Combine the results from the above steps to write the final simplified expression. The simplified expression is \(36 * x^2\) or \(36x^2\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Power Rule
The power rule is a fundamental concept in algebra that simplifies the process of managing exponents. When applying the power rule to expressions, each component within a set of parentheses is raised to the specified power. For example, in the expression \((-6x)^2\), both \(-6\) and \(x\) are raised to the power of 2. This results in the expression \((-6)^2 \cdot x^2\). The power applies to both the coefficient \(-6\) and the variable \(x\), illustrating how the power rule helps break down complex expressions.

This rule is especially helpful when working with polynomials or any expressions involving products raised to a power.
  • Raise each factor inside the parentheses to the specified power individually.
  • Reconstruct the expression using these results.
Simplifying Expressions
Simplifying expressions is a key skill in algebra that involves reducing expressions into their simplest forms. This makes it easier to understand and work with them in further calculations. For the expression \((-6x)^2\), the goal is to break it down into easily manageable parts and then combine them.

The simplification process involves several steps:
  • First, apply rules like the power rule to distribute exponents.
  • Next, compute any numerical calculations required, such as squaring the coefficient \(-6\), resulting in \(36\).
  • Finally, combine all parts into one expression, i.e., \(36x^2\), which is neater and more straightforward to use.
Each of these steps reduces the complexity of the original expression, helping to convey more meaning at a glance.
Squares
Squares are a fundamental mathematical operation where numbers or expressions are multiplied by themselves. When squaring, we often encounter expressions like \( (-6x)^2 \). Here, both the coefficient \(-6\) and the variable \(x\) are squared.

Calculating the square of a number means multiplying it by itself. For \((-6)^2\), we calculate \(-6 \times -6 = 36\). This explains why squaring a negative number results in a positive number. This operation helps convert multiplication and addition into a form that can be efficiently managed in equations.
  • The square of an expression is calculated by multiplying it by itself.
  • This process retains the nature of the expression while providing a multiplied form.
  • Perfect squares, like \(36\), are often easy to recognize, simplifying computation.
Understanding squares is essential when simplifying expressions or solving equations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Perform the indicated operations. $$(y+5)^{2}-(y-4)^{2}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$4^{-2}<4^{-3}$$

Find each of the products in parts (a)-(c). a. \((x-1)(x+1)\) b. \((x-1)\left(x^{2}+x+1\right)\) c. \((x-1)\left(x^{3}+x^{2}+x+1\right)\) d. Using the pattern found in parts (a)-(c), find $(x-1)\left(x^{4}+x^{3}+x^{2}+x+1\right) without actually multiplying.

We have seen that in \(2009,\) the United States government spent more than it had collected in taxes, resulting in a budget deficit of \(\$ 1.35\) trillion. a. Express 1.35 trillion in scientific notation. b. A trip around the world at the Equator is approximately \(25,000\) miles. Express this number in scientific notation. c. Use your scientific notation answers from parts (a) and (b) to answer this question: How many times can you circle the world at the Equator by traveling 1.35 trillion miles?

Explain how to divide monomials. Give an example.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.