Sure, let's determine which one of the given expressions is a monomial.
A monomial is an algebraic expression that consists of only one term. That term may be a constant, a variable, or a product of constants and variables with non-negative integer exponents.
Let's analyze each option:
A. [tex]\(20 x^{11} - 3x\)[/tex]:
- This expression consists of two terms, [tex]\(20 x^{11}\)[/tex] and [tex]\(-3x\)[/tex].
- Since it has more than one term, it is not a monomial.
B. [tex]\(11 x - 9\)[/tex]:
- This expression consists of two terms, [tex]\(11x\)[/tex] and [tex]\(-9\)[/tex].
- Since it has more than one term, it is not a monomial.
C. [tex]\(\frac{9}{x}\)[/tex]:
- This can be rewritten as [tex]\(9x^{-1}\)[/tex] which involves a negative exponent.
- Monomials cannot have negative exponents, so this is not a monomial.
D. [tex]\(20 x^{11}\)[/tex]:
- This expression consists of a single term and the exponent [tex]\(11\)[/tex] is a non-negative integer.
- This fits the definition of a monomial.
Therefore, the correct answer is:
D. [tex]\(20 x^{11}\)[/tex]
