A monomial is a single term consisting of a constant, a variable, or a product of constants and variables raised to non-negative integer powers.
NoteMonomials are the building blocks of polynomials. Understanding how to manipulate them is essential for working with more complex algebraic expressions.
Multiplying Monomials
To multiply monomials, follow these steps:
- Multiply the coefficients (the numerical parts).
- Multiply the variables by adding their exponents (using the laws of exponents).
When dividing variables, make sure the exponent in the numerator is greater than or equal to the exponent in the denominator. Otherwise, the result will involve negative exponents or fractions.
Self review1. Multiply \$2x^3y^2\$ and \$5x^2y^4\$. 2. Divide \$15x^6y^3\$ by \$3x^2y\$.
Theory of KnowledgeHow do the laws of exponents reflect the fundamental properties of numbers? Can you think of other areas in mathematics where similar rules apply?
NoteBe careful with negative exponents and fractions. They require additional rules and are not covered in this section.
Self review1. Multiply \$2x^3y^2\$ and \$5x^2y^4\$. 2. Divide \$15x^6y^3\$ by \$3x^2y\$.
Theory of KnowledgeHow do the laws of exponents reflect the fundamental properties of numbers? Can you think of other areas in mathematics where similar rules apply?
NoteBe careful with negative exponents and fractions. They require additional rules and are not covered in this section.
