1. What Is a Monomial?

A monomial is a mathematical expression consisting of a single term which is a product of numbers, variables, and positive integer exponents. Examples include 3x², -5xy³, or 7.

2. How To Calculate a Monomial

The general form of a monomial is:

Where:

• Coefficient — A constant number multiplying the variables
• Variables — Letters representing unknown quantities (x, y, etc.)
• Exponents — Positive integers indicating the power of each variable

Calculation Steps:

1. Multiply the coefficient by each variable raised to its exponent
2. If evaluating for specific values, substitute the values for the variables
3. Perform the exponentiation and multiplication operations

3. Components of a Monomial

Key Characteristics:

• Single term only (no addition or subtraction)
• Variables have whole number exponents (0, 1, 2, 3,...)
• Can have multiple variables (e.g., 3x²y³z)
• Degree is the sum of all exponents (for 4xy²z³, degree = 1+2+3 = 6)

4. Using the Calculator

Instructions:

1. Enter the coefficient (number part)
2. Enter variables separated by commas (e.g., x,y)
3. Enter corresponding exponents separated by commas (e.g., 2,3)
4. Optionally enter values for variables to evaluate the monomial
5. Click Calculate to see the monomial expression and value

5. Frequently Asked Questions (FAQ)

Q1: Can a monomial have negative exponents?
A: No, by definition monomials only have non-negative integer exponents.

Q2: Is a single number like 5 considered a monomial?
A: Yes, constants are monomials with zero-degree (x⁰ = 1).

Q3: What's the difference between monomial and polynomial?
A: A polynomial is a sum of monomials, while a monomial has just one term.

Q4: How do you multiply monomials?
A: Multiply coefficients and add exponents of like variables (3x² × 4x³ = 12x⁵).

Q5: Can a monomial have fractional coefficients?
A: Yes, coefficients can be any real number (including fractions).