To determine which of the given expressions is a monomial, let's recall the definition of a monomial. A monomial is an algebraic expression that consists of only one term. This term can include a constant (coefficient), a variable, and a non-negative integer exponent.
Let's analyze each option one by one:
Option A: [tex]\(11x - 9\)[/tex]
- This expression has two terms: [tex]\(11x\)[/tex] and [tex]\(-9\)[/tex].
- Since it has more than one term, it is not a monomial.
Option B: [tex]\(\frac{9}{x}\)[/tex]
- This expression can be written as [tex]\(9x^{-1}\)[/tex], where the variable [tex]\(x\)[/tex] has an exponent of [tex]\(-1\)[/tex].
- For an expression to be a monomial, the exponent of the variable must be a non-negative integer. Here, the exponent is negative.
- Therefore, this is not a monomial.
Option C: [tex]\(20x^9 - 7x\)[/tex]
- This expression has two terms: [tex]\(20x^9\)[/tex] and [tex]\(-7x\)[/tex].
- Since it has more than one term, it is not a monomial.
Option D: [tex]\(20x^9\)[/tex]
- This expression has only one term: [tex]\(20x^9\)[/tex].
- The coefficient is [tex]\(20\)[/tex] and the variable [tex]\(x\)[/tex] is raised to the power of [tex]\(9\)[/tex] (a non-negative integer).
- Since it meets the criteria of having only one term with a non-negative integer exponent, it is a monomial.
Therefore, the correct answer is:
D. [tex]\(20x^9\)[/tex]
