/*! 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 37 Identify the base and the expone... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 37

Identify the base and the exponent in each expression. $$2 x^{3}$$

Short Answer

Expert verified
In the term \(2 x^{3}\), the base and exponent of the sub-expression \(2\) are 2 and 1, respectively, and the base and exponent of the sub-expression \(x^3\) are \(x\) and 3, respectively.

Step by step solution

01

Identify the base and exponent in \(2^1\)

The first sub-expression is 2, which is actually an abbreviation for \(2^1\). So, the base here is 2, and the exponent is 1.
02

Identify the base and exponent in \(x^3\)

The second sub-expression is \(x^3\). Here, the base is \(x\), and the exponent is 3.

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.

Base and Exponent
Let's talk about what a base and an exponent are in mathematical expressions. When you see something like \(2^3\), the number 2 is called the base, and the number 3 is the exponent. The base is the number or variable that is being multiplied by itself, and the exponent tells you how many times to multiply it.
For example:
  • In \(2^3\), the base is 2. This means you multiply 2 by itself.
  • The exponent is 3. This means you should multiply 2 by itself 3 times.
To solve \(2^3\), you calculate \(2 \times 2 \times 2\), which equals 8. Understanding this concept helps you simplify expressions and solve algebraic problems.
Algebraic Expressions
Algebraic expressions are puzzles made up of numbers and variables combined using mathematical operations. In the expression \(2x^3\), you're seeing an algebraic term with a number (2) and a variable (x).
The number 2 here is called a coefficient. It multiplies the base, which in this part of the expression is the variable \(x\) with the exponent 3. When you see such an expression:
  • The coefficient is the numeric factor that is not tied to a variable's exponent.
  • The base, in this context, can be a variable like \(x\).
  • The exponent expresses how many times to use the base in a multiplication.
Understanding these terms is crucial when dealing with multivariable algebraic expressions.
Mathematical Notation
Mathematical notation is like the language used to write and communicate math ideas clearly and efficiently. Using symbols reduces lengthy descriptions, making it simpler to understand complex problems at a glance. For example, in the notation \(x^3\):
  • \(x\) is a variable, representing an unknown value in problems.
  • \(^3\) indicates the power to which \(x\) is raised.
In this framework, equations and expressions follow specific rules, allowing consistency and reducing errors when solving problems. Proper understanding of notation bridges the gap between mathematical theory and practical application, enabling clearer communication of ideas.

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

Perform the operations. $$-2 a b+7 a b-3 a b$$

Simplify or solve as appropriate. $$4+(2 y-3)^{2}=(2 y-1)(2 y+3)$$

Give an example of a polynomial that is \(\ldots\) a binomial

$$\text { If } x=105, \text { evaluate } \frac{x^{500}-x^{499}}{x^{499}}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.