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NAME:_________________________________________________ Algebra 2: Lesson 9-3 Rational Exponents DATE:____________ Learning Goals 1. How do we evaluate expressions with rational exponents? 2. How do we rewrite rational exponents as radicals? DO NOW: Simplify the following expressions. Use a calculator if needed. 1. √ 2. √ 3. √ 4. 5. 6. Based on the questions above, how can you rewrite the expressions below? √ Exercise #1: Rewrite each of the following using radicals, and then simplify, if possible. 1. 2. 3. 4. ( ) 5. 6. 7. 8. ( ) A rational exponent does not have to be in the form . Other rational numbers, such as or can also be used as exponents. Let’s think about the expression . Evaluate this expression in two different ways by using the laws of exponents. Then verify these answers with your calculator. Rational Exponent Definition For any rational number we define to be ___________ or ___________ Exercise #2: Rewrite each of the following using radicals, and then simplify, if possible. 1. 4. ( ) 2. 3. 5. 6. PRACTICE 1. Yoshiko said that she is or is not correct. because is one-fourth of . Use properties of exponents to explain why 2. Rita said that because , so exponents to explain why she is or is not correct. 3. Suppose for some positive real number that ( , and then ) . What is the value of ? 4. Simplify the expression and write your answer using a positive exponent. . Use properties of 5. Simplify the expression below and write your answer using positive exponents only. 6. Evaluate the function 7. Evaluate the function at ( ). for .