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The degree of a term is the exponent of the variable within that term. Let's consider the term from the exercise: \( 7z \). Here, the variable is \( z \). When a variable is written without an explicit exponent, it is understood to have an exponent of 1. So, \( z \) is the same as \( z^1 \). Therefore, the degree of the term \( 7z \) is 1.

Understanding the degree of a term is crucial in algebra because it helps us categorize and compare different terms. For example, in a polynomial, terms are often arranged based on their degree. Terms with higher degrees are placed before those with lower degrees. If you're dealing with multiple terms, identifying the degree of each term will help you simplify and solve algebraic expressions more accurately.

Intermediate algebra includes topics that build on basic algebra concepts and prepare students for advanced math. One of these topics is understanding and working with numerical coefficients and variable exponents.

In intermediate algebra, you will frequently encounter terms like coefficients, variables, and exponents, which are fundamental building blocks for more complex equations and functions. For example, in the term \( 7z \), 7 is the numerical coefficient and \( z \) is the variable. Together, they form a term that can be part of larger algebraic expressions or equations.

Intermediate algebra also deals with solving equations and inequalities, simplifying expressions, and understanding polynomials. Mastering these concepts will make it easier to tackle higher-level algebra and calculus problems.

A variable exponent is the power to which a variable is raised in a term. In the term \( 7z \), the variable \( z \) has an exponent of 1, even though it is not explicitly written. Understanding variable exponents is essential because they impact the degree of the term.

When you see terms like \( z^2 \) or \( x^3 \, y \), the exponents (2 and 3) tell you how many times the variable is used as a factor. Exponents also play a pivotal role in polynomial equations, where each term has a variable raised to a certain power.

For example, in the polynomial \( 3x^2 + 5x + 7 \), the exponents of the variables are 2 and 1, respectively. This information helps in simplifying and solving algebraic expressions. Knowing the variable exponents makes it easier to add, subtract, and even multiply terms correctly.