/*! 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 7 Find the degree of each term. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 7

Find the degree of each term. \(-8^{7} y^{3}\)

Short Answer

Expert verified
The degree of the term is 3.

Step by step solution

01

Identify Each Component

The given term is \(-8^7 y^3\). This term has a numerical coefficient \(-8^7\) and a variable part \(y^3\).
02

Determine the Degree of the Variable Part

The variable \(y\) is raised to the power of 3, which means its degree is 3. For the purpose of the degree of the term, only consider the variable's exponent.

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
Understanding exponents is a key part of algebra. An exponent indicates how many times a number, known as the base, is multiplied by itself. For example, in \(8^7\), 8 is the base and 7 is the exponent. This means you multiply 8 by itself 6 more times: 8 \(\times 8 \times 8 \times 8 \times 8 \times 8 \times 8\).
This operation simplifies large calculations and expressions, making them easier to understand and manipulate.
When dealing with polynomial terms, we often look at the exponent of the variable to determine the degree of the term.
Polynomial terms
A polynomial term consists of numbers and variables combined using multiplication and possibly raised to powers. Each separate part of a polynomial is known as a term. For example, the term \(-8^7 y^3\) is a single entity within a larger polynomial.
Polynomial terms can vary in complexity, featuring variables raised to various powers, and coefficients that can dramatically affect their properties like their degree or value. What remains critical is understanding how each component contributes to the term's overall identity.
Coefficient and variable
In a polynomial term like \(-8^7 y^3\), understanding the distinction between coefficients and variables can clarify many algebraic processes.
The coefficient is the numerical factor of a term, which is \(-8^7\) in this case. It serves as a multiplier for any variable components. Coefficients are crucial because they offer weight and scale to the term.
Meanwhile, the variable, represented by \(y\), carries the power that determines the degree of the term. This variable can change and thus makes the term polynomic. Working with both elements helps solve equations and evaluate expressions effectively.
Algebra fundamentals
Algebra serves as the language of mathematics, creating a system for solving equations and expressing mathematical ideas. It utilizes symbols and sets the groundwork for advanced math topics. Understanding algebraic terms and structures, such as polynomial expressions, illuminates the problem-solving process.
The foundational concepts like coefficients, variables, and powers form the basis upon which more complex algebraic reasoning is constructed.
  • Algebra allows us to manipulate expressions to simplify them or to solve for unknowns.

  • Identifying various components like the degree of a term becomes critical in analyzing and organizing polynomials.

  • Algebra fosters logical thinking, equipping us with tools for a broad range of scientific and daily problems.

Mastering algebra fundamentals is key to advancing in mathematics and understanding the detailed exercises seen in textbooks.

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

Factor each polynomial completely. See Examples 1 through 12. $$ x^{2}+6 x y+5 y^{2} $$

Recall that a graphing calculator may be used to check addition, subtraction, and multiplication of polynomials. In the same manner, a graphing calculator may be used to check factoring of polynomials in one variable. For example, to see that $$ 2 x^{3}-9 x^{2}-5 x=x(2 x+1)(x-5) $$ graph \(\mathrm{Y}_{1}=2 x^{3}-9 x^{2}-5 x\) and \(\mathrm{Y}_{2}=x(2 x+1)(x-5) .\) Then trace along both graphs to see that they coincide. Factor the following and use this method to check your results. $$ x^{4}+6 x^{3}+5 x^{2} $$

Factor each polynomial completely. See Examples 1 through 12. $$ x^{2}+4 x+5 $$

Factor. Assume that variables used as exponents represent positive integers. $$ 36 x^{2 n}-49 $$

Without calculating, determine which number is larger. $$ 7^{-11} \text { or } 7^{-13} $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.