Please open your laptops, log in to the MyMathLab course web site, and open Daily Quiz 24.

1. Please open your laptops, log in to the MyMathLab course web site, and open Daily Quiz 24. • A scientific calculator may be used on this quiz. • Remember to turn in your answer sheetto the TA when the quiz time is up.

2. Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials.

3. Reminder to teachers: You can use item analysis to see which questions your section missed most on last Thursday’s Weekly Quiz, and you can insert slides here with screen shots of those questions you want to go over in class. It may also be helpful if you use the “export data” function on the Practice Weekly Quiz (export all attempts) to get an idea of how many times the average student took the practice quiz and how many didn’t take it at all – there seemed to be a lot of those this time around…

4. Weekly Quiz 6 Results: • Average class raw score: __________ • Average class score after partial credit: _______ (Letter grade: ___) • Practice quiz data: • Average number of attempts: _______ • Average best score: _______ • Maximum number of attempts: _______ • Number of students who didn’t take it: _______ • (Remember, the weekly practice quiz is a required, 4-point assignment!) • Commonly missed questions: #_______________ Grade Scale

5. Quiz question # ____ (xx%)

6. Section 5.5A Negative Exponents

7. When might you have to deal with a negative exponent? Example: Use the quotient rule to simplify (Assume that x ≠ 0.) Solution: But what does x-2mean? So:

8. In order to extend the quotient rule to cases where the difference of the exponents would give us a negative number we define negative exponents as follows: If a  0, and n is an integer, then

9. Example 1) 2) Remember that without parentheses, only the x is the base for the exponent –4, not the entire expression 2x. 3) Simplify by writing each of the following expressions with positive exponents. (Calculate out any number terms.)

10. Note that in the previous problem, 2x-4 • gave us 2 on top and x4 on the bottom, • andonly the x term, not the 2, • was raised to the -4th power. • Here’s a question for you: • What would (2x)-4 look like when simplified? • Would it look different than 2x-4? • (Good question for a quiz!)

11. Watch out for negatives that are NOT in the exponent! For example: What’s the difference between 3-1and-3?

12. 1) 2) Notice the difference in results when parentheses enclose the -3 3) More examples with negative signs in exponents and other negative signs that are notin the exponent: Simplify by writing each of the following expressions with positive exponents or calculating:

13. Problem from today’s homework: Solution: 1/6 + 1/25 = 31/150

14. Example 1) 2) Simplify by writing each of the following expressions with positive exponents. (Note that to convert a power with a negative exponent to one with a positive exponent, you simply switch the power from a numerator to a denominator, or vice versa, and switch the exponent to its positive value.)

15. Problem from today’s homework: Answer: 5 . x9z8

16. Example from today’s homework: Answer: 7 . 9xy13

17. Example from today’s homework:(do this in your notebook) Answer: 16 . x12y40

18. Power of a Quotient Quotient Rule for exponents Negative exponent Summary of exponent rules If m and n are integers and a and b are real numbers, then: Product Rule for exponentsam• an = am+n Power Rule for exponents(am)n = amn Power of a Product(ab)n = an• bn Zero exponenta0 = 1, a 0

19. Example Simplify the following expression, using only positive exponents in your answer. Note: Problems like this are much easier to solve if you start by simplifying the part inside the parentheses by combining the exponents of identical bases using the quotient rule, and then apply the power rule using the exponent outside of the parentheses . = (3-2- -4 a3-7 b1- - 3)-2 = (32 a -4 b 4)-2 = 32*-2 a-4*-2 b4*-2 = 3-4 a8 b-8 = a 8 34b8 = a8 81b8

20. REMINDER: The assignment on today’s material (HW 28) is due at the start of the next class session. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in on the Math 110 clipboard by the front door of the lab

21. You may now OPEN your LAPTOPS and begin working on the homework assignment. We expect all students to stay in the classroom to work on your homework till the end of the 55-minute class period. If you have already finished the homework assignment for today’s section, you should work ahead on the next one or work on the next practice quiz/test.