Answer :
To determine which of the given expressions is a monomial, we first need to understand what a monomial is. A monomial is an algebraic expression that consists of only one term. This term can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.
Let's evaluate each option:
A. [tex]\(\frac{9}{x}\)[/tex]
- This is not a monomial because it involves division by the variable [tex]\(x\)[/tex], which means [tex]\(x\)[/tex] is in the denominator. This form is not allowed in monomials.
B. [tex]\(20x - 14\)[/tex]
- This expression consists of two terms: [tex]\(20x\)[/tex] and [tex]\(-14\)[/tex]. Since a monomial can only have one term, this is not a monomial.
C. [tex]\(20x^9 - 7x\)[/tex]
- This expression consists of two terms: [tex]\(20x^9\)[/tex] and [tex]\(-7x\)[/tex]. Since a monomial can only have one term, this is not a monomial.
D. [tex]\(11x^2\)[/tex]
- This expression consists of a single term: [tex]\(11x^2\)[/tex]. It is in the form of a constant multiplied by a variable raised to a non-negative integer power. Therefore, this is a monomial.
After evaluating all the options, the expression that is a monomial is:
[tex]\[ \boxed{11x^2} \][/tex]
Let's evaluate each option:
A. [tex]\(\frac{9}{x}\)[/tex]
- This is not a monomial because it involves division by the variable [tex]\(x\)[/tex], which means [tex]\(x\)[/tex] is in the denominator. This form is not allowed in monomials.
B. [tex]\(20x - 14\)[/tex]
- This expression consists of two terms: [tex]\(20x\)[/tex] and [tex]\(-14\)[/tex]. Since a monomial can only have one term, this is not a monomial.
C. [tex]\(20x^9 - 7x\)[/tex]
- This expression consists of two terms: [tex]\(20x^9\)[/tex] and [tex]\(-7x\)[/tex]. Since a monomial can only have one term, this is not a monomial.
D. [tex]\(11x^2\)[/tex]
- This expression consists of a single term: [tex]\(11x^2\)[/tex]. It is in the form of a constant multiplied by a variable raised to a non-negative integer power. Therefore, this is a monomial.
After evaluating all the options, the expression that is a monomial is:
[tex]\[ \boxed{11x^2} \][/tex]
