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