Question

question 9 of 10
which of the following is a monomial?

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

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

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

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

Explanation:

Step1: Recall the definition of a monomial

A monomial is a single term consisting of a product of a constant (coefficient) and variables raised to non - negative integer powers. It can also be a single constant or a single variable.

Step2: Analyze Option A

For the expression \(\frac{9}{x}\), we can rewrite it as \(9x^{- 1}\). Since the exponent of \(x\) is \(- 1\), which is a negative integer, this is not a monomial (it is a rational expression, specifically a reciprocal of a variable times a constant).

Step3: Analyze Option B

The expression \(20x^{9}\) is a product of a constant \(20\) and a variable \(x\) raised to the non - negative integer power of \(9\). It is a single term, so it is a monomial.

Step4: Analyze Option C

The expression \(20x^{9}-7x\) has two terms (\(20x^{9}\) and \(-7x\)) separated by a subtraction sign. So, it is a binomial (a type of polynomial with two terms), not a monomial.

Step5: Analyze Option D

The expression \(11x - 9\) has two terms (\(11x\) and \(-9\)) separated by a subtraction sign. So, it is a binomial, not a monomial.

Answer:

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