1. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

2. Math 110 Final Exam: Comprehensive – covers the whole semester Worth 200 points (20% of course grade) 45 questions Test period is one hour and 50 minutes Practice Final will be worth 10 points and also has 45 questions and unlimited tries. Your best score on the practice final will also earn up to 20 extra credit points on the final. (more details next week)

3. Make sure you know the day and time of the final exam for this section of Math 110: All Math 110 finals will be given in your regular classroom. (Next slide shows final exam schedules for all sections.)

4. Wednesday 12/16Thursday 12/17Friday 12/18Monday 12/21 Tuesday 12/22 8:00 to 10:00 Scheduled Final in 214: LAB CLOSED 110-001 Neiderhauser 8:00110-002 Lee 10:10010-003 DKL MW 12:20110-005 Lee 2:30 10:00 to 12:00 Scheduled Final in 245: 010-004 Corne TTh 2:30 12:00 to 2:00 Scheduled Final in 214: 110-006 Lee 3:35010-001 DKL MW 9:05110-003 Schmidt 11:15110-004 Thielman 1:25 2:00 to 4:00 Scheduled Final in 214: LAB CLOSED 010-002 Mayer TTh 9:05 4:00 to 6:00 Scheduled Final in 214: 110-007 Hulett 4:40 6:00 to 8:00 Scheduled Final in 214: LAB CLOSED 110-008 Hulett 5:45

5. Section 10.2 Radicals and Rational Exponents

6. If n is a positive integer greater than 1 and a is a real number, then Definition of a rational exponent in terms of a radical:

7. Recall that a cube root is defined so that However, if we let b = a 1/3, then Since both values of b give us the same a, Why does this definition make sense?

8. Use radical notation to write the following. Simplify if possible. Example

9. We can expand our use of rational exponents to include fractions of the type m/n, where m and n are both integers, n is positive, and a is a positive number,

10. Use radical notation to write the following. Simplify if possible. Example

11. Problem from today’s homework: 64

12. Now to complete our definitions, we want to include negative rational exponents. If a -m/n is a nonzero real number,

13. Use radical notation to write the following. Simplify if possible. Example What if the previous problem was ? The answer would be “N” (not a real number) because you’d be trying to take an even root of a negative number.

14. All the properties that we have previously derived for integer exponents hold for rational number exponents, as well. We can use these properties to simplify expressions with rational exponents.

15. Use properties of exponents to simplify the following. Write results with only positive exponents. Example What would this answer look like in radical form?

16. Problem from today’s homework: Final answer: -b Hint: The exponent will be 2/5 + 1/5 – (-2/5). Then simplify the fraction.

17. Use rational exponents to write as a single radical. Example

18. Problem from today’s homework: Final answer: Hints: Start by writing each radical as a rational (fraction) exponent, then add the fractions by finding a common denominator. For your final step, convert back into radical form.

19. The assignment on this material (HW 10.2) is due at the start of the next class session. You may now OPEN your LAPTOPS and begin working on the homework assignment until the end of the class period.