1. Rational Exponents N.RN.2 – Rewrite expressions involving radicals and rational exponents using properties of exponents. N.RN.3 – Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

2. How to play… When a new problem is shown, write down your answer on a slip of paper (write it BIG) Do not show your answer to anyone! When the teacher says “SHOWDOWN” slap your answer down for everyone to see. Discuss your answers with your group, come to an agreement on the correct answer

3. Showdown

4. Sets of Real Numbers

5. Always, Sometimes, Never 1.The sum of two rational numbers is rational 2.The product of two rational numbers is a whole number 3.The sum of a rational number and an irrational number is rational 4.The product of a nonzero rational number and an irrational number is irrational

6. Always, Sometimes, Never 1.The sum of two rational numbers is rational (A) 2.The product of two rational numbers is a whole number (S) 3.The sum of a rational number and an irrational number is rational (N) 4.The product of a nonzero rational number and an irrational number is irrational (A)

7. Properties of Exponents NamePropertyExample Product of Powers Quotient of Powers Power of a Product Power of a Quotient Power of a Power Negative Exponent

8. The “nth” root of a RadicandIndex

9. Properties of Radicals NamePropertyExample Radical of a Product Radical of a Quotient Radical of a Radical

10. Rational Exponents & Radicals ExponentRadicalExample

12. With your partner…

13. Example 3: Simplify each expression. Express solutions in radical form (where necessary).

14. Example 4. In parts B & C, you started with an expression in radical form, converted to rational exponent form, and then converted back to radical form. Explain the purpose of each conversion.

15. Example 5.

16. Example 6.

19. Exit Card