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Degree of a Monomial

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Degree of a Monomial

Study Guide

Key Definition

The degree of a monomial is the sum of the exponents of all its variables. For example, the degree of the monomial $7y^3z^2$ is $5$ because $3 + 2 = 5$.

Important Notes

The degree of a constant is always $0$.
For a monomial like $7x$, the degree is $1$.
The degree of $66$ is $0$.
In the expression $7y^3z^2$, add the exponents of $y$ and $z$.
Remember, no variable means the degree is $0$.
The degree of a nonzero constant is $0$; the zero monomial's degree is undefined.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$y^n$ indicates y raised to the power n

Remember to use proper notation when solving problems

Why It Works

The degree of a monomial provides a quick way to understand the highest power of the variable terms, which is crucial for understanding polynomial behavior and solving equations involving monomials.

Remember

The degree of a monomial is the sum of its variable exponents.

Quick Reference

Degree of a nonzero constant:$0$

Degree of a single-variable monomial:$n$ where n is the exponent

Degree of $7y^3z^2$:$5$

Understanding Degree of a Monomial

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Video explanation of this concept

Beginner

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Beginner Explanation

The degree of a monomial is simply the sum of the exponents of all its variables. For example, in $7x^2$, the degree is $2$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the degree of the monomial $6x^3y^2$?

Real-World Problem

Question Exercise

Intermediate

Degree Calculation

Compute the degree of the monomial $x^2y^3$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the monomial $5x^4y$. How would the degree change if the exponent of $y$ was increased by $2$?

Challenge Quiz

Single Choice Quiz

Advanced

Determine the degree of the monomial $3x^2y^4z^5$.

Recap

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