Do Now

Laws of Exponents -Evaluating Exponents MAFS.8.EE.1.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27  Explain the properties of integer exponents to generate equivalent numerical expressions.  Apply the properties of integer exponents to produce equivalent numerical expressions.

Symbols ▪ When you see this symbol… copy the notes from this slide into your math journal. ▪ When you see this symbol, use the whiteboards to complete the problem.

Today’s Goals and Agenda By the end of class today I will: Know properties of integer exponents and be able to create equivalent numerical expressions I plan to do this by: ▪ I Do: Laws of Exponents Notes ▪ We Do: Mini White board Practice ▪ You Do: Begin Home Learning Assignment

Laws of Exponents What is a monomial? (number)(variable) (The product of numbers and variable(s))

3 3 4 y 3 Exponents!

What is an exponent? A quantity representing the power to which a given number or expression is to be raised. Example: 4³ means to multiply four by itself 4 times. So, 4³ =______ ∙ ______∙______=______

Zero Power Law and Negative Exponent Law

Write out the terms as they appear in exponential form with answer Hints! -An exponent tells how many times a number or variable is being multiplied! -Anything to the power of zero is 1! -A number raised to a negative exponent is it’s opposite or reciprocal! We Do:

Do NOW ▪ A cube has side lengths of 6 units. Write an integer expression to express the volume of the cube. ▪ What if you had 2 cubes both with side lengths of 7 units, write an exponential integer for each cube and then multiply the two expressions. Explain the steps that you would take to find the product of the two volumes.

Laws of Exponents -Product of Powers/Quotient of Powers

Today’s Goals and Agenda By the end of class today I will: Know the Product of Powers,Quotient of Powers, Power of a Power and Power of a Product Properties I plan to do this by: ▪ I Do: Laws of Exponents Notes ▪ We Do: Mini White board Practice ▪ You Do: Properties Foldable

Write This Down: Product of Powers Multiplying Rule: When multiplying monomials, multiply the base and add the exponents. Remember!, a monomial can be a number, a variable, or the product of numbers and variables. Product of Powers Property

NUMBERS VARIABLES PRODUCT OF NUMBERS AND VARIABLES 2 (4) = _______ Product of Powers Law: When multiplying monomials, multiply the coefficients and add the exponents Adding the exponents. Multiplying coefficients AND adding exponents.

Try These on Your White Board! NUMBERS VARIABLES PRODUCT OF NUMBERS AND VARIABLES We Do:

Quotient of Powers Property The opposite of division is ______________. And when multiplying monomials, the rule tells says to ________ the coefficients and _____ the exponents. Because division and multiplication are opposites, when dividing monomials, ______ the coefficients and ________ the exponents. multiplication divide add multiply subtract Write This Down: Quotient of Powers Property

DIVIDING RULE: Divide the coefficients and subtract the exponents NUMBERS VARIABLES PRODUCT OF NUMBERS AND VARIABLES Subtract exponents Adding the coefficients and subtracting the exponents.

Try These on Your White Board NUMBERS VARIABLES PRODUCT OF NUMBERS AND VARIABLES Subtract exponents Adding the coefficients and subtracting the exponents. We Do:

DO NOW

Laws of Exponents - Powers of Powers & Power of a Product

When raising a monomial to a power, raise everything to the power. Coefficients get raised to a power and exponents get multiplied. (Multiplying Monomials Part 2) Write this Down! Power of a Power Property

Power of a Power Law When multiplying, the exponents are added together. Unless! The exponent(s) are located outside the parenthesis. Everything inside the parenthesis has to be raised to that outside power. NUMBERS VARIABLES PRODUCT OF NUMBERS AND VARIABLES 3(5)² = 3(__)(___) 5 5 inside outside inside outside

We Do:

On Your White Board!

Write this Down! Power of a Product Law

Write this in Your Notes! #1 There must be two or more variables or constants that are being multiplied together. In the example below, those are the m and n, but they could be any variable or constant. #2 The result of the multiplication problem must be raised to a power. In the below example, that is the 5. Two Conditions for Power of a Product Law:

You Do: Foldable Instructions ▪ You should have one flap for each of the following 1.Negative Power Property 2. Zero Power Property 3.Product of Powers Property 4.Quotient of Powers Property 5.Power of a Power Property 6.Power of a Product Property Each Flap need to include a definition of the Property and at least one example with solution.

Home Learning ▪ Finish your foldable! ▪ Start studying your notes for your Unit 1 Exam! ▪ Review your Laws of Exponents Notes, you never know if they’ll be a pop quiz Monday- hint hint