Question

which expression is a monomial?

\\(\bigcirc\\) \\(\frac{1}{x}\\)

\\(\bigcirc\\) \\(3x^{0.6}\\)

\\(\bigcirc\\) \\(x + 1\\)

\\(\bigcirc\\) \\(7\\)

Explanation:

🆕 New Concept Discovered: Identifying Monomials
A single term with non-negative integer exponents

Step 1: Define a monomial

A monomial is an algebraic expression consisting of one term. For an expression to be a monomial, it must be a number, a variable, or a product of numbers and variables. Crucially, any variables in a monomial must have exponents that are non-negative integers (such as \(0, 1, 2, 3, \dots\)).

This means:

• No variables in the denominator (which represents a negative exponent).
• No fractional or decimal exponents on variables.
• No addition or subtraction of separate terms.

Step 2: Analyze each option

• Option 1: \(\frac{1}{x}\)

This can be written as \(x^{-1}\). Because the exponent is negative (or because the variable is in the denominator), this is not a monomial.

• Option 2: \(3x^{0.6}\)

The exponent on the variable \(x\) is \(0.6\). Since \(0.6\) is a decimal and not an integer, this is not a monomial.

• Option 3: \(x + 1\)

This expression consists of two terms separated by an addition sign. This is a binomial, not a monomial.

• Option 4: \(7\)

This is a constant number. A constant is considered a monomial of degree \(0\) (it can be thought of as \(7x^0\)). Therefore, this is a monomial.

Answer:

\(7\)