To determine which of the following expressions is a monomial, let's start by figuring out what a monomial is.
A monomial is a single term consisting of a constant, a variable, or the product of a constant and one or more variables raised to non-negative integer exponents. In other words, a monomial cannot have multiple terms, fractions with variables in the denominator, or negative exponents.
Let's evaluate each option:
Option A: [tex]\( 20x^9 \)[/tex]
- This expression is a single term.
- It consists of a constant (20) and a variable (x) raised to a non-negative integer exponent (9).
- Therefore, [tex]\( 20x^9 \)[/tex] is a monomial.
Option B: [tex]\( 20x^9 - 7x \)[/tex]
- This expression has two terms: [tex]\( 20x^9 \)[/tex] and [tex]\(-7x\)[/tex].
- Since a monomial can have only one term, [tex]\( 20x^9 - 7x \)[/tex] is not a monomial.
Option C: [tex]\( \frac{9}{x} \)[/tex]
- This expression involves a variable (x) in the denominator.
- A monomial cannot have a variable in the denominator.
- Therefore, [tex]\( \frac{9}{x} \)[/tex] is not a monomial.
Option D: [tex]\( 11x - 9 \)[/tex]
- This expression has two terms: [tex]\( 11x \)[/tex] and [tex]\(-9\)[/tex].
- Since a monomial can have only one term, [tex]\( 11x - 9 \)[/tex] is not a monomial.
Given this analysis, the correct answer is Option A, [tex]\( 20x^9 \)[/tex], as it is the only expression that meets the criteria of being a monomial.
