/*! 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 138 How many \(4 a^{2} x^{3}\) 's ar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 138

How many \(4 a^{2} x^{3}\) 's are there in \(-16 a^{4} x^{5}\) ?

Short Answer

Expert verified
Answer: \(-4a^2x^2\)

Step by step solution

01

Divide coefficients

First, we will divide the coefficients of the given expressions. Divide \(-16\) by \(4\) to get \(-4\).
02

Divide variables with respect to exponent

Next, we want to divide the variables separately. Starting with 'a', divide \(a^4\) by \(a^2\). Using the rule \(\frac{a^n}{a^m} = a^{n-m}\), we get \(a^{4-2} = a^2\). Similarly, divide \(x^5\) by \(x^3\). Following the same rule, we get \(x^{5-3} = x^2\).
03

Combine the results

Now, combine the results from Step 1 and Step 2. We get \((-4)(a^2)(x^2)\) which simplifies to \(-4a^2x^2\). So, there are \(-4a^2x^2\) times \(4a^2x^3\)'s in \(-16a^4x^5\).

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.

Exponents
Exponents are a way to represent repeated multiplication of a number. When you see something like \(a^4\), it means you multiply \(a\) by itself four times (i.e., \(a \times a \times a \times a\)). Exponents follow specific rules that help us simplify algebraic expressions. One important rule is the division of exponents used in expressions like \(\frac{a^n}{a^m} = a^{n-m}\). This rule helps us in simplifying expressions by subtracting the exponent of the divisor from the exponent of the dividend, which was crucial in solving the given exercise.
Dividing Coefficients
Coefficients are the numerical parts of terms in an algebraic expression. In our exercise, the terms \(4a^2x^3\) and \(-16a^4x^5\) have coefficients 4 and -16, respectively. Dividing coefficients involves simply dividing the numbers. For instance, when dividing \(-16\) by \(4\), you perform regular division to get \(-4\). This easy step is essential as it separates the numerical part from the variable part, allowing us to focus separately on the variables using exponent rules.
Combining Like Terms
Combining like terms is a fundamental aspect of simplifying algebraic expressions. Like terms have the same variable parts, meaning both the variables and their exponents must match. For instance, \(3x^2\) and \(5x^2\) are like terms because they both have \(x^2\). In the exercise solution, we first simplified the expression by dividing each component and combined the resulting terms to get \(-4a^2x^2\). It's important to remember that only like terms can be combined to get a simpler form.
Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and exponents connected by operations like addition, subtraction, multiplication, and division. The exercise involves dividing two algebraic expressions \(4a^2x^3\) from \(-16a^4x^5\). Such expressions can be simplified using mathematical operations and rules like the ones for exponents and coefficients. Algebraic expressions are essential parts of algebra and understanding how to handle them, including simplifying through division, is vital for solving many math problems.

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

For the following problems, perform the multiplications and combine any like terms. $$ 5 y^{6}(y+7)(y+1) $$

For the following problems, simplify each of the algebraic expressions. $$ x y(3 x y+2 x-5 y)-2 x^{2} y^{2}-5 x^{2} y+4 x y^{2} $$

For the following problems, answer the question of how many. $$ c^{3} \text { 's in } 2 a^{2} b c^{3} ? $$

Find the product. \((4 x+3)(4 x-3)\).

For the following problems, perform the multiplications and combine any like terms. $$ 8\left(c^{3}+5 c+11\right) $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.