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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.
A single-term expression is a monomial only if all of its variables have whole numbers — non-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. 5x/y^2 = 5xy^(- 2) 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 |
|---|---|
| 5 | Any constant is a valid monomial. By the Zero Exponent Property, 5x^0=5. |
| 0 | The coefficient of a monomial can be 0. |
| - 2x^5 | The coefficient can be negative. |
| x^3y/5 | 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 |
|---|---|
| 2x^(- 1) | The variables of a monomial cannot have negative integer exponents. |
| 4x^3/y | Monomials cannot have variables in the denominator. |
| 5 x^3y^(12) | The variables of a monomial must only have whole number exponents. |