How to Multiply Monomials

By Christine Lehman

A monomial is an algebraic value that has only a single term, but can be made of a combination of numbers or variables. An example of a monomial would be 4xy. There can also be exponents within monomials, but they must always be positive, whole integers. Polynomials are made up of two or more monomials. Binomials contain two monomials, and trinomials contain three monomials. There are several rules that need to be taken into consideration when multiplying monomials.

How to multiply monomials

Understand what an exponent is. An exponent is also known as power and is denoted as follows: 4^2. The number 4^2 is read four to the second power, or four squared and is calculated by multiplying the four with itself the number of times of the exponent. So, 4^2 = 16. When multiplying monomials, exponents are always added with one another. So, 4^2 * 4^2 = 4^4.

Understand what a base is. The base is the number that is being raised to a power. For example, in the expression 5^2, the number 5 is the base. When multiplying monomials, bases are always multiplied with one another. So, 3x * 3x = 9x^2

Multiply the bases of the monomials together. For example, consider (5x^2y) * (6x4y^3). Begin by multiplying the bases of x (5 and 6) together to get 30. Then multiply the bases of y (1 and 4) to get 4.

Add the exponents together. In the above example, (5x^2y) * (6x4y^3) add the exponents of both the x and y values. The exponent on the x value would be 3 (2 + 1) and the value on the y exponent would be 4 (1 + 3). The final answer for the example is 30x^3y4^4.