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Properties of Exponents -Integer Exponents

Today’s Goals and Agenda By the end of class today I will: Know properties of integer exponents and be able to define them with examples. I plan to do this by: ▪ I Do: Properties of Exponents Notes ▪ We Do: Mini White board Practice ▪ You Do: Foldable and Begin Home Learning Assignment

What is an exponent? 3 4 y 3

Write this Down What are exponents? An Exponent tells us to multiply a number by itself by the number of times the exponent is. Example: 4³ means to multiply four by itself 4 times. So, 4³=______∙______∙______=______

Write this Down Zero and Negative Exponent

We Do: Pull out your White Board Write out the answer to the following terms 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!

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) = _______ Multiplying Rule: 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

Dividing Monomials 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 MONOMIALS: 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.

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 (Tomorrow) 6.Power of a Product Property (Tomorrow) ▪ Each Flap need to include a definition of the Property and at least one example with solution.

Home Learning ▪ Spring Board Page 290 – Numbers ▪ Spring Board Page 293 – Numbers 12-18

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

Today’s Goals and Agenda By the end of class today I will: Know the Power of a Powers and Powers of a Product Properties well enough to evaluate exponential exponents. I will also be introduced to the concept of rational exponents I plan to do this by: ▪ I Do: Power of Powers/Power of a Product Notes ▪ We Do: Finish Foldable ▪ You Do: Start Home Learning

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) Pull Out your Foldable! 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

Pull Out Your Foldable! 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:

Write this in Your Notes! Exponents that are fractions. Rational Exponents “B” can be any real number greater than zero, “n” is any integer greater than 1.

Examples:

Write this in your Notes! “B” can be any nonzero number. “M” and “N” can be any integers as long as “n” > 1, Rational Exponents (cont.)

Explained Some More… When you are dealing with a radical expression, you can convert it to an expression containing a rational (fractional) power. This conversion may make the problem easier to solve.

Notice there are 3 different ways to write a rational exponent Example:

Pull Out your White Boards!

Example: ▪ Write the following expression as a radical What is your base/radicand? x What is your exponent? 3 What is your index? 2

On Your White Board Rewrite as a Radical: Base? Exponent? Index? Bases are 3 and y. Exponent is 1. Index is 3.

On Your White Board Rewrite as a Radical: Base? Exponent? Index? There are two bases: 24 and x 24: exponent is 1 & index is 4 x : exponent is 2 & index is 4

More Examples: or

Examples: or Write this in Your Notes! Negative Rational Exponents

On Your Board: Use the properties of exponents to simplify each expression

We Do: Rational Exponents Cont. Rewrite the following expression using a single radical: How? To be in the same radical they have to have the same index (denominator). Find a common denominator!! The Common Denominator would be 6 Now rewrite using a radical with an index of 6. Remember which exponent goes with which base!

Home Learning ▪ Spring Board Activity 19 Practice: pg ▪ Choose 3 problems to solve from: – Lesson 19-1 – Lesson 19-2 – Lesson 19-3 ▪ You should turn in 9 problems total, show your work! ▪ Study for your Exam and Review Rational Exponents Notes- You might have a quiz Monday hint hint