# Aim: How do we divide monomials?

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Aim: How do we divide monomials?
10/4 Aim: How do we divide monomials? Do Now: List three things everyone should know about exponents.

Three things everyone should know about exponents.
1) Parentheses matter: 2) Anything to the zero power equals 1. x0 = Well almost anything 3) Negative exponents do not negate the base they move it!

Three things everyone should know about exponents.
1) Parentheses matter: 2) Anything to the zero power equals 1. x0 = Well almost anything 3) Negative exponents do not negate the base they move it!

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: 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. Remember: A number divided by itself is 1.

Dividing Monomials For all real numbers a, and integers m and n:

Dividing Monomials Ex 1: Simplify using positive exponents only

Dividing Monomials Ex 2: Simplify using positive exponents only

Dividing Monomials Ex 3: Simplify using positive exponents only

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.

Fractions to a Power For all real numbers a and b, and integer m:

Practice Ex 4: Simplify using positive exponents only

Problem 1

Practice Ex 5: Simplify using positive exponents only

Problem Ahh! THINK! x2-2 = x0 = 1

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