Unit 1 Day 3 Rational Exponents Objectives: Simplify a rational expression with radicals by rationalizing the denominator (include applying the conjugate). Rewrite and evaluate a radical with rational exponents, and a number with a rational exponent in radical notation. Use properties of rational exponents to evaluate and simplify expressions. Standards: Supplementary Reading:

Warmup Convert the following into exponential or radical form. Query Question: Turn the following Root into a Rational exponent

Important Vocabulary Radical Radicand Index Root Rational Exponent Denominator Numerator Rationalize Conjugate Square Cube

Simplifying Radicals Radical Expressions have rules to follow in order to be simplified. 1.) cannot have perfect number factors. 2.) cannot have fraction under radical. 3.) cannot have radical numbers in denominator. **May need to multiply by conjugate** **Using DOSquares or S&DOCubes**  

Examples  

Examples  

Examples  

Simplifying Rational Exponents Rational Exponents follow the same rules as radicals and integer exponents. 1.) cannot have rational exponents in denominator 2.) cannot have fraction as base of rational exponent. 3.) cannot have negative exponents  

Operating W/ Rational Exponents

Check For Understanding Simplify Answer Answer

Problem 1 Example1:          

Problem 2 Example 2:              

Partner Work

Partner Work

Closure Simplify the following expression.   Homework: None!

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