Dividing Monomials

Objectives Be able to divide polynomials Be able to simplify expressions involving powers of monomials by applying the division properties of powers.

Vocabulary Monomial: A number, a variable, or the product of a number and one or more variables Constant: A monomial that is a real number. Power: An expression in the form xn. Base: In an expression of the form xn, the base is x. Exponent: In an expression of the form xn, the exponent is n. Quotient: The number resulting by the division of one number by another.

Review: Exponents Repeated multiplication can be represented using exponents. To expand a power, use the exponent to determine the number of times a base is multiplied by itself.

Review: Multiplying Monomials Product of Powers: When two numbers with the same base are multiplied together, add the exponents and leave the base unchanged. Power of a Product: In a product raised to a power, the exponent applies to each factor of the product.

Review: Multiplying Monomials Power of a Power: When a power is raised to another power, multiply the exponents and leave the base unchanged. Remember: Follow the order of operations when applying more than one property!

Quotient of Powers Simplify: Step 1: Rewrite the expression in expanded form Step 2: Simplify. For all real numbers a, and integers m and n: Remember: A number divided by itself is 1.

Power of a Quotient Simplify: Step 1: Write the exponent in expanded form. For all real numbers a and b, and integer m: Step 2: Multiply and simplify.

Example Problems Apply quotient of powers. Apply power of a quotient. Apply power of a power Simplify

Practice 1. 2.

Problem 1

Problem 2 THINK! x2-2 = x0 = 1