Question

State the following statement is true or false.
A monomial is a product of powers of variables with non-negative integer exponents

Answer 1

Hint: A monomial is a polynomial that contains a singular term which can be a number, a variable or a product of numbers and variables. It contains no negative or fractional exponents for that would prevent it from being the classic definition of a monomial.

Complete step-by-step solution:
Polynomials are equations or algebraic expressions that consist of variables and and/or coefficients and have one or more terms in it. They have different names depending on the number of terms. If a polynomial consists of only one term, it’s called a monomial. When it consists of two terms, it’s called a binomial. When it consists of three terms, it’s called a trinomial. When it consists of more than three terms, it’s usually referred to as a polynomial.
By definition, the involvement of operations of addition, subtraction, multiplication and non-negative integer exponents of variables is present for polynomials.
For a monomial to be considered a monomial, it has to have a single term which is a non-zero term. Since it consists of only a single term, it’s easier to perform operations of addition, subtraction, and multiplication with monomials. Monomials can’t have a variable in the denominator, they consist of only one variable, or a coefficient, or a product of coefficients and variables.
For example, $4xy,5,6x,y$ are all monomials.
Hence it is True that A monomial is a product of powers of variables with non-negative integer exponents.

$\therefore$ The given statement is true.

Note: Any variable fraction cannot be a monomial as monomials can’t have a variable in the denominator. The degree of a monomial is the sum of the exponents of all the included variables which forms monomials.