Module 0 Part 2: Exponents and Radicals Obj: To revisit prior knowledge about exponents and radicals Evi: Students will be able to solve exponent and radical.

Slides:



Advertisements
Similar presentations
Simplify Radical Expressions
Advertisements

COMPLEX NUMBERS Objectives
Simplifying Radical Expressions Product Property of Radicals For any numbers a and b where and,
Roots & Radical Exponents By:Hanadi Alzubadi.
Drill #63 Find the following roots: Factor the following polynomial:
5.6 Radical Expressions Rationalizing the denominator Like radical expressions Conjugates.
Binomial Radical Expressions
7.1, 7.2 & 7.3 Roots and Radicals and Rational Exponents Square Roots, Cube Roots & Nth Roots Converting Roots/Radicals to Rational Exponents Properties.
5.7 Complex Numbers 12/17/2012.
Write out on the board how to do them using radicals!!! The PP has how to solve using powers….you show how to use radicals!!! 1.
Rational Exponents and Radicals
Chapter 6 Radical Functions and Rational Exponents.
Review Laws of Exponents
Simplifying When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals.
Identify the perfect square in each set , 81, 27, , 99, 8, , 84, 12, , 216, 196, 72 Find the Prime Factorization of.
 Form of notation for writing repeated multiplication using exponents.
5.5 Roots of Real Numbers and Radical Expressions.
R Review of Basic Concepts © 2008 Pearson Addison-Wesley. All rights reserved Sections R.5–R.7.
Warm ups. Find the sum or difference SOLVING RATIONAL EXPRESSIONS AND REVIEW Objective: To review adding, subtracting, and solving rational expressions.
Simplifying When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals.
Simplify Radical Expressions. EQs…  How do we simplify algebraic and numeric expressions involving square root?  How do we perform operations with square.
5.7 Complex Numbers 12/4/2013. Quick Review If a number doesn’t show an exponent, it is understood that the number has an exponent of 1. Ex: 8 = 8 1,
Simplifying Radical Expressions Basic multiplication Basic division o Rationalize the denominator.
Adding and Subtracting Radical Expressions
Exponents and Radicals Objective: To review rules and properties of exponents and radicals.
3.2 Apply Properties of Rational Exponents Do properties of exponents work for roots? What form must they be in? How do you know when a radical is in simplest.
GOAL: USE PROPERTIES OF RADICALS AND RATIONAL EXPONENTS Section 7-2: Properties of Rational Exponents.
Conjugate of Denominator
Conjugate: Value or that is multiplied to a radical expression That clears the radical. Rationalizing: Removing a radical expression from the denominator.
Exponents and Radicals Section 1.2. Objectives Define integer exponents and exponential notation. Define zero and negative exponents. Identify laws of.
7-2 Properties of Rational Exponents (Day 1) Objective: Ca State Standard 7.0: Students add, subtract, multiply, divide, reduce, and evaluate rational.
Objectives: Students will be able to… Use properties of rational exponents to evaluate and simplify expressions Use properties of rational exponents to.
Bellwork. Survey results:  Students who voted for online homework: 84%  Students who voted for paper homework: 16%  Students who wants to keep group.
Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.4 – Complex Numbers.
6.2A- Operations for Fractions Adding & Subtracting – Create a COMMON DENOMINATOR – ADD or SUBTRACT 2 TOPS (Numerators) – KEEP the common denominator (bottom)
Complex Numbers n Understand complex numbers n Simplify complex number expressions.
Slide Copyright © 2012 Pearson Education, Inc.
5.6 Radical Expressions Objectives: 1.Simplify radical expressions. 2.Add, subtract, multiply and divide radical expressions.
7.5 Operations with Radical Expressions. Review of Properties of Radicals Product Property If all parts of the radicand are positive- separate each part.
7.2 Properties of Rational Exponents Do properties of exponents work for roots? What form must they be in? How do you know when a radical is in simplest.
Rational (Fraction) Exponent Operations The same operations of when to multiply, add, subtract exponents apply with rational (fraction) exponents as did.
Roots, Radicals, and Root Functions
Section 7.1 Rational Exponents and Radicals.
R-6 How are Exponents & Radicals Simplified?
Adding and Subtracting Rational Expressions
Radical Expressions and Rational Exponents
Unit #2 Radicals.
Simplifying Radical Expressions
Apply Exponent Properties Involving Quotients
Operations with Rational (Fraction) Exponents
Do-Now: Simplify (using calculator)
Simplifying Radical Expressions
Warmup.
Drill #
6.7 Imaginary Numbers & 6.8 Complex Numbers
In other words, exponents that are fractions.
Rational Exponents Section 6.1
Simplifying Radical Expressions
Dividing Radical Expressions.
Simplifying Radical Expressions
Simplifying Radical Expressions
Simplify Radical Expressions
10.1 Radical Expressions and Graphs
Warmup Find the exact value. 1. √49 2. –√144.
5.2 Properties of Rational Exponents and Radicals
3.2 Apply Properties of Rational Exponents
Simplifying Radical Expressions
Simplifying Radical Expressions
Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.
P.3 Radicals and Rational Exponents
Presentation transcript:

Module 0 Part 2: Exponents and Radicals Obj: To revisit prior knowledge about exponents and radicals Evi: Students will be able to solve exponent and radical problems

Exponent Notation If a is a real number and n is a positive integer, then Where n is the number of factors (or a’s) and is the exponent and a is the base. It is read as “a to the n th power”

Exponent Properties Zero Power One Power Product Property Quotient Property Power Property

Radicals Holds true for n greater than or equal to 2. a is a real number

The thing about Radicals is… The most important thing to know about radicals is how to simplify An expression involving radicals is in simplest form when the following conditions are satisfied 1. All possible factors have been removed from the radical 2. All fractions have radical-free denominators 3. The index of the radical is reduced

Two different ways to simplify Way 1 1. Write out all basic factors (Factor tree that #) 2. Group by what size the root is. (Pairs, groups of three…) 3. Pull out 1 of the #s from each group 4. Repeat till you can’t do anymore

Way 1 Example

Way 2 The Damon Way This is too complex to show on slide…

Way 2 Example

Combining Radicals or How to add and subtract Radical expressions can be added or subtracted if they are like radicals (same root and same # in the root) Example Step 1: Simplify Individual Radicals Step 2: Simplify Step 3: Add or subtract Step4: DONE

Hair in your Chipotle Burrito Imagine going to Chipotle and ordering a burrito and finding a hair in your burrito would you keep eating it? Probably it is Chipotle Having a radical in the denominator is the same thing!!!! What can we do about this metaphorical hair in our denominator/burrito

Option 1: Take Hair out/Rationalize!!!! Rationalizing is when you multiply the numerator and denominator by the radical on the bottom and then simplify Example

Option 2: Dissect Burrito to see if other hair exists/Multiply by the Conjugate If your denominator has two terms you have to multiply by the conjugate Conjugate examples: Conjugate is

Conjugate Example Step 1: Multiply by the Conjugate Step2: FOIL the denominator Step 3: Simplify denominator Step 4: Simplify the whole enchilada I am hungry now Homework: On class page