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Today: 1. Hand back/review Test 2 2. Lecture on Section 5.1, with HW 5.1 due tomorrow 3. Daily Quiz (Test 2 Review) last 10 minutes of class

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Note: There are 56 problems in The HW 5.1 assignment, but most of them are very short. (This assignment will take most students less than an hour to complete.)

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Grade Scale Test 2 Results: Average class score after partial credit: __________ Commonly missed questions: #_________________ If you got less than 75% on Test 2, make sure to go over your test with me or a TA sometime in the next few days. This material will be used in the next unit, and it will also be covered again on the final exam.

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Teachers: You can insert screen shots of any test problems you want to go over with your students here. Also, make sure to start quiz with at least 10 minutes left in class period. QuizReview Test 2 has a 10-minute time limit..

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

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Section 5.1 Exponents

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Exponents that are natural numbers are shorthand notation for repeating factors. 3 4 = 3 3 3 3 3 is the base 4 is the exponent (also called power) Note, by the order of operations, exponents are calculated before all other operations, except expressions in parentheses or other grouping symbols.

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Product Rule (applies to common bases only) a m a n = a m+n Simplify each of the following expressions. Example 3 2 3 4 = 3 6 = 3 3 3 3 3 3= 729 x 4 x 5 = x 4+5 z 3 z 2 z 5 = z 3+2+5 (3y 2 )(-4y 4 )= 3 y 2 -4 y 4 = (3 -4)(y 2 y 4 )= -12y 6 = 3 2+4 = x 9 = z 10

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Zero exponent a 0 = 1, a 0 Note: 0 0 is undefined. Simplify each of the following expressions. 5 0 Example = 1 (xyz 3 ) 0 = x 0 y 0 (z 3 ) 0 = 1 1 1 = 1 -x0-x0 = -1x 0 = -1 1 = -1 (Assume all variables have nonzero values.)

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Problem from todays homework:

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Quotient Rule (applies to common bases only) Example Simplify the following expression. Group common bases together

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Problem from todays homework:

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Power Rule: (a m ) n = a mn Note that you MULTIPLY the exponents in this case. Example Simplify each of the following expressions. (2 3 ) 3 = 2 9 = 512 (x4)2(x4)2 = x 8 = 2 33 = x 42

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Compare the result of (2 3 ) 3 to the result of 2 3 2 3: 2 3 2 3 = 2 3+3 = 2 6 = 64 Compare the result of (x 4 ) 2 to the result of x 4 x 2 : x 4 x 2 = x 4+2 = x 6 CAUTION: Notice the importance of considering the effect of the parentheses in the preceding example.

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Power of a Product Rule (ab) n = a n b n Simplify (5x 2 y) 3 Example = 5 3 (x 2 ) 3 y 3 = 125x 6 y 3

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Example from todays homework: (do this in your notebook) Answer: 36 a 18

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Power of a Quotient Rule Example Simplify the following expression. (Power of product rule in this step) (Power rule in this step)

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(All of these are on your formula sheet use it while you do the homework.) Summary of exponent rules If m and n are integers and a and b are real numbers, then: Product Rule for exponents a m a n = a m+n Power Rule for exponents (a m ) n = a mn Power of a Product (ab) n = a n b n Power of a Quotient Quotient Rule for exponents Zero exponent a 0 = 1, a 0

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The assignment on todays material (HW 5.1) is due at the start of the next class session. Please open your laptop and pull up Quiz Review Test2. When you finish the quiz, you are free to leave or go into the open lab to work on your online homework. Lab hours in 203: Monday Thursday, 8:00 a.m. to 6:30 p.m. Please remember to sign in! You may use the pink formula sheet on this quiz please dont write on this sheet, and remember to hand it back in with your quiz answer sheet.