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
Slide 2
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.)
Slide 3
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.
Slide 4
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..
Slide 5
Please CLOSE YOUR LAPTOPS, and turn off and put away your cell
phones, and get out your note- taking materials.
Slide 6
Section 5.1 Exponents
Slide 7
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.
Slide 8
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
Slide 9
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.)
Slide 10
Problem from todays homework:
Slide 11
Quotient Rule (applies to common bases only) Example Simplify
the following expression. Group common bases together
Slide 12
Problem from todays homework:
Slide 13
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
Slide 14
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.
Slide 15
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
Slide 16
Example from todays homework: (do this in your notebook)
Answer: 36 a 18
Slide 17
Power of a Quotient Rule Example Simplify the following
expression. (Power of product rule in this step) (Power rule in
this step)
Slide 18
(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
Slide 19
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.