In mathematics, a monomial is, roughly speaking, a polynomial [polynomial] which has only one term (a). Two definitions of a monomial may be encountered:

  1. A monomial, also called power product, is a product of powers of variables (a) with nonnegative integer (a) exponents, or, in other words, a product of variables, possibly with repetitions. For example, \(x^{2}yz^{3} = xxyzzz\) (a) is a monomial. The constant \(1\) (a) is a monomial, being equal to the empty product (a) and to \(x^{0}\) (a) for any variable \(x\) (a). If only a single variable \(x\) (a) is considered, this means that a monomial is either \(1\) (a) or a power \(x^{n}\) (a) of \(x\) (a), with \(n\) (a) a positive integer. If several variables are considered, say, \(x,y,z,\) (a) then each can be given an exponent, so that any monomial is of the form \(x^{a}y^{b}z^{c}\) (a) with \(a,b,c\) (a) non-negative integers (taking note that any exponent \(0\) (a) makes the corresponding factor equal to \(1\) (a)).
  2. A monomial is a monomial in the first sense multiplied by a nonzero constant, called the coefficient (a) of the monomial. A monomial in the first sense is a special case of a monomial in the second sense, where the coefficient is \(1\) (a). For example, in this interpretation \(- 7x^{5}\) (a) and \((3 - 4i)x^{4}yz^{13}\) (a) are monomials (in the second example, the variables are \(x,y,z,\) (a) and the coefficient is a complex number (a)).

(“Monomial” 2022)