/*! 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 11 Write the given expression witho... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 11

Write the given expression without exponents. $$x y^{3}$$

Short Answer

Expert verified
x y y y

Step by step solution

01

Identify the exponent

In the expression \(x y^{3}\), identify the exponent which is 3 in \(y^{3}\).
02

Expand the base using the exponent

Expand the base (\(y\)) by multiplying it by itself as many times as the exponent indicates. Thus, \(y^{3}\) becomes \(y \times y \times y\).
03

Combine the result

Combine \(x\) and the expanded expression of \(y\). The expanded form of \(x y^{3}\) is \(x \times y \times y \times y\).

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.

Expanding Exponents
Understanding how to expand exponents is crucial in algebra. An exponent tells you how many times to multiply a number by itself. For instance, in the expression \( y^3 \), the exponent is 3. This means you multiply the base, which is \( y \), by itself three times. So, \( y^3 \) becomes \( y \times y \times y \).
Expanding exponents helps to simplify expressions and make algebraic operations clearer. Here, instead of dealing with \( y^3 \), you can handle it as \( y \times y \times y \), which sometimes makes it easier to combine with other terms or perform further calculations.
Multiplication
Multiplication is a basic mathematical operation where you combine multiple quantities together. When expanding exponents, you essentially perform a series of multiplications. For example, in the expanded form of \( y^3 \), you multiply \( y \) by itself three times: \( y \times y \times y \).
In algebra, terms can include numbers, variables, or both. When you see an expression like \( x y^3 \), it means you are multiplying \( x \) by \( y \times y \times y \). Combining these together gives you \( x \times y \times y \times y \). This step ensures every part of the expression is accounted for and properly expanded.
Variables
Variables are symbols used to represent numbers in algebra. They are often letters like \( x \) or \( y \). Variables can stand for unknown values or values that can change. In the expression \( x y^3 \), both \( x \) and \( y \) are variables.
When working with variables, you treat them like numbers in arithmetic operations. For expanding exponents, it鈥檚 important to recognize what the variables represent and how to manipulate them. In our example, \( y^3 \) means \( y \times y \times y \), so when combined with \( x \), you get \( x \times y \times y \times y \). Understanding variables and how to expand them using exponents can clarify complex algebraic expressions.

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

Discuss what is wrong (if anything) with each of the following examples: (a) \(5-3(x-4) \stackrel{?}{=} 2(x-4) \stackrel{?}{=} 2 x-8\) (b) \(5-3(x-4) \stackrel{2}{=} 5-3 x-4 \stackrel{2}{=} 1-3 x\) (c) \(5-3(x-4) \geq 5-3 x-12 \frac{2}{2}-7-3 x\) (d) \(5-3(x-4) \geq 5-3 x+12 \leq 17-3 x\)

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$x-(y-z)$$

Examine each of the following expressions as given and determine the number of terms. Also find the coefficient and the literal part of each term. $$2 a^{2}+7 a-3$$

Simplify by combining like terms whenever possible. $$0.8 x-5-x+2.7$$

Simplify by combining like terms whenever possible. $$5 x\left(x^{2}+3\right)+2 x\left(3+x^{2}\right)$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

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.