Unit 1 Day 2 Rational Exponents Objectives: Use properties of rational exponents to evaluate and simplify expressions. Use properties of rational exponents to solve real-life problems. Standards: Supplementary Reading:

Unit 1 Outline Theme: Roots, Rational Exponents & Complex #s 1.) Simplifying & operating w/ roots 2.) Defining a rational exponent 3.) operations w/ rational exponents 4.) defining the imaginary number & complex #s 5.) taking powers of the imaginary number 6.) operating w/ complex numbers Essential Questions: A. What is the relationship b/w radicals & rational exponents? B. Why are rational exponents needed? C. Why should radical expressions be simplified? D. When must complex #s be applied to radical expressions? Unit 1 Quiz: Thursday Sept 24th Unit 1 Test: Wednesday Sept 30th

Warmup Query Question: Name one of the 3 rules of simplifying radicals In your own words. What do you think a rational exponent means? Use your calculator & plug in values to create a conjecture.   Query Question: Name one of the 3 rules of simplifying radicals

Important Vocabulary Exponent Rational Radical Inverse

Lets Discuss What are inverses & identities? Types of identities: Additive Multiplicative Exponential Types of inverses: How does it relate to an integer exponent? How do roots and rational exponents compare? **Note** there are different types of inverses, for numbers, operations, functions & more

Defining Rational Exponents  

Check For Understanding   Answer Answer

Defining Rational Exponents  

Operating W/ Rational Exponents What happens when you add expressions with rational exponents? What happens when you subtract expressions with rational exponents? What happens when you multiply expressions with rational exponents? What happens when you divide expressions with rational exponents? What happens when you take the power of expressions with rational exponents?

Lets Experiment

Operating W/ Rational Exponents

Simplifying Rational Exponents Same rules apply to rational exponents as integer exponents & radicals. No negatives allowed No perfect factors left in expression No rational exponents in denominator No Fractions w/in the rational exponent.

Example

Check For Understanding Simplify Answer Answer

Problem 1 Example1:          

Problem 2 Example 2:                  

Classwork Start on homework. You may work with the group you are sitting with.

Closure Homework: What was not Finished in class! How do properties of roots relate to laws of exponents? Homework: What was not Finished in class!

Unit 1 test question How do properties of roots relate to laws of exponents