Algebra Period 4

Multiplying and Dividing Monomials 5-3

A monomial is an expression that is either a numeral, a variable , or a product of numerals and variables with whole number exponents. IF the monomial is just a numeral we call is a constant.

Some examples: 4x³, -7ab, y (1/2)x⁵ and 2x⁴y

The following are NOT monomials
1/y, x^1/2, x² +4, y² + 2y + 4

Multiplying monomials - use the properties of rational numbers and the properties of exponents:
(3x)(4x) = 12x²

(3x²)(-x) = (3x²)(-1x)
= (3)(-1)(x²)(x)
=-3x³

(-3a)(4a²)(-a⁴ = (-3)(4)(-1)(a)(a²)(a)
=12a⁷

Dividing is similar-- Use the properties of rational numbers and the properties of exponents:

x⁵/x² = x^5-2 = x³

4x²/5x⁷ = (4/5)x^2-7 = (4/5)x^-5 OR
(4/5x⁵)

12m⁵/4m³ = 3m²
BUT
4m⁵/12m³ = m²/3

Be careful Keep the RULES Separate!! Don't mix up your exponent RULES with what you know previously for rational numbers!!