Standard Form of a Polynomial
Concept

Monomial

A monomial is an algebraic expression consisting of only one term. It is a product of powers of variables and a constant called the coefficient.
The monomial 2x^2y^3 with a coefficient of 2, and variables x and y.
A single-term expression is a monomial only if all of its variables have whole numbersnon-negative and integers — as exponents. However, variables with positive exponents in the denominator are excluded because they are equivalent to a power in the numerator with the opposite exponent, according to the Quotient of Powers Property. Consider the following example.
In other words, if a variable in the denominator of an expression, it is not a monomial. The following are valid examples of monomials.
Expression Why It Is a Monomial
Any constant is a valid monomial. By the Zero Exponent Property,
The coefficient of a monomial can be
The coefficient can be negative.
A monomial can have numbers in the denominator.

Although they appear to be monomials at first glance, the single-term expressions in the following table do not satisfy the definition of a monomial.

Expression Why It Is Not a Monomial
The variables of a monomial cannot have negative integer exponents.
Monomials cannot have variables in the denominator.
The variables of a monomial must only have whole number exponents.
Exercises