Question

question 1 of 10
which of the following is a monomial?

a. \\(\frac{9}{x}\\)

b. \\(20x^9 - 7x\\)

c. \\(11x - 9\\)

d. \\(20x^9\\)

Explanation:

Step1: Recall Monomial Definition

A monomial is a single term, which can be a number, a variable, or a product of numbers and variables (with non - negative integer exponents). It cannot have negative exponents or be a sum/difference of terms.

Step2: Analyze Option A

For option A, \(\frac{9}{x}=9x^{- 1}\). Since the exponent of \(x\) is \(- 1\) (a negative integer), it is not a monomial.

Step3: Analyze Option B

Option B is \(20x^{9}-7x\). This is a sum of two terms (\(20x^{9}\) and \(-7x\)), so it is a binomial, not a monomial.

Step4: Analyze Option C

Option C is \(11x - 9\). This is a sum of two terms (\(11x\) and \(-9\)), so it is a binomial, not a monomial.

Step5: Analyze Option D

Option D is \(20x^{9}\). It is a single term, with a number \(20\) and a variable \(x\) raised to a non - negative integer exponent (\(9\)). So it fits the definition of a monomial.

Answer:

D. \(20x^{9}\)