How to Simplify Monomials

Students learn how to simplify monomials in algebra.
••• Zimiri/iStock/Getty Images

To solve polynomial expressions, you may need to simplify monomials -- polynomials with only one term. Simplifying monomials follows a sequence of operations involving rules for handling exponents, multiplying and dividing. Always handle variables with exponents raised to a power first.

Definitions of Terms

The base is a variable, and an exponent is the power a variable is raised to. A variable with no visible exponent is assumed to have an exponent of 1. A variable with an exponent of zero is equal to the value 1. A coefficient is a number that precedes a variable and is a multiplier of that variable; for example, in 7y, the 7 is the coefficient.

Rules for Simplifying Monomials

The power of a power rule says that when evaluating a power of a power, multiply the exponents of base variables. The multiply monomials rule says that when you multiple monomial expressions, add the exponents of like bases. The dividing monomials rule says that when you divide monomials, subtract the exponents of like bases.

An Example

The expression x^y means x to the y power, for example: 2^3 equals 2 times 2 times 2, which yields 8.

An example of simplifying monomials using the power of a power rule might be: [3x^3 y^2]^2 = 9x^6 y^4. If x = 2 and y = 3, on the left side of the equation, you have: 2^3 = 8, 3 times 8 = 24, 3^2 = 9, 9 times 24 = 216 and 216^2 = 46,656. On the right side of the equation, you have: x^6 = 64, 9 times 64 = 576, 3^4 = 81 and 81 times 576 = 46,656.

Related Articles

How to Manipulate Roots & Exponents
How to Get Rid of Cubed Power
How to Integrate the Cube Root of X
How to Calculate the Volume of a Cylinder
How to Calculate the Area of a Curved Surface
How to Simplify Exponents
How to Find the Height of a Rectangular Pyramid
How to Divide Exponents With Different Bases
How to Do Exponents Outside of the Parenthesis
How to Find Resistance With Power & Voltage
The Foil Method With Fractions
What Does YX Mean on a Calculator?
How to Solve Rational Expression Equations
How to Calculate the Area of a Base
How to Factorise a Quadratic Expression
How to Help With Polynomials
How to Interconvert Moles, Molarity and Volume
How to Divide Rational Numbers
How to Classify Polynomials by Degree
How to Find Equations of Tangent Lines