How to Simplify Expressions With Variable Exponents

Instructor: Maria Blojay

Maria has taught College Algebra and has a master's degree in Education Administration.

In this lesson, we will learn how to simplify expressions with variable terms that have exponents, with the help of some basic algebra terminology. Some of the key terms we will review are grouping and combining like terms.

What Does Simplifying an Expression Using Variables Mean?

Before we get started, let's first review some important math vocabulary that we need to know to help us with our lesson.

To get a better understanding of the process of simplifying expressions involving variables, let us first take apart the words to see what each truly means, and how each work together to complete the problem.

An algebraic expression is a list of one or more variable, constants, and operational symbols.

A monomial is an expression in which variables and constants may be by themselves or be multiplied with others.

The terms of an algebraic expression are its monomials. A term that has a variable being part of it is a variable term. A term that has no variable is a constant term.

When a term is a result of a number and a power of a variable, the number portion is called a coefficient.

Like terms are terms with the same variable part types.

In this example,

Sample Trinomial With Parts

Notice that the 5x2 and 7x are variable terms. 11 represents a constant term

So, to simplify an expression is to produce an answer that has no groups of terms that are alike after those terms were combined.

The example above is a simplified variable expression.

Simplify Expressions With Variable Exponents

We will now take a look at four examples of how to simplify the expression with variable terms that have exponents.

Example 1

Simplify this expression:

Ex1Prob1

Here, we have two variable terms in which 7 and 2 are coefficients. 11 is a constant.

These two variable terms have this power, which is made up of a base and exponent, x2 in common. So, these are considered like terms.

We then group the coefficients together surrounding them with grouping symbols - parentheses, and then simplify the expression by combining like terms.

example 1

Constant terms are terms that are alike but have different values. Also, notice the 11 is NOT combined with the other variable terms and the 2s of the exponents are NOT combined.

Example 2

Simplify this expression:

Ex2S1

Use the Distributive Property -

Remember the Distributive Property: a(b +c) = ab + ac , for example: 3(x + 2) = 3(x) + (3)(2) = 3x + 6

E2S2

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