Test 1 Results:
•Average class score after partial credit: XX.X%
•Commonly missed questions: # _________________
Grade Scale
Grade
A
A-
B+
B
B-
C+
C
Points
≥ 925
≥ 900
≥ 875
≥ 825
≥ 800
≥ 775
≥ 725
% Score
≥ 92.5
≥ 90
≥ 87.5
≥ 82.5
≥ 80
≥ 77.5
≥ 72.5
C-
F
≥ 700
< 700
≥70
< 70
All of this material will be tested again on the
final exam, so please make sure you go over the
problems you missed with a teacher or TA.
The Home Stretch:
Final topic: 5 sections from Chapter 5 on
exponents and polynomials
Next quiz: Quiz 3 on sections 5.1-5.4 and 5.6
Last classes: In-class review sessions for the
final, with two 20-point review homework
assignments.
Final Exam: Comprehensive, 200 points,
during evaluation week.
Check your syllabus to find the date and time
of the final exam for this section.
If you haven’t passed the Gateway yet, make
sure you take it this week.
Gateway Quiz Retake Times
(One new attempt allowed per week, beginning March 7)
• Mondays
– 1:25 pm
– 2:30 pm
• Tuesdays
– 10:10 am
– 11:15 am
• Wednesdays
– 10:10 am
– 11:15 am
• Thursdays
– 1:25 pm
– 2:30 pm
SIGN UP IN THE MATH TLC OPEN LAB!
If NONE of the above times work for you…
email Krystle Mayer, Math TLC Coordinator (JHSW 201) or Dr.
Laura Schmidt, to set up a date and time.
Please
CLOSE
YOUR LAPTOPS,
and turn off and put away your
cell phones,
and get out your notetaking materials.
Section 5.1:
Working with Exponents
• Exponents that are natural numbers are
shorthand notation for repeating factors.
•
•
•
34 = 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 parentheses.
Example
Evaluate each of the following expressions.
34 = 3 • 3 • 3 • 3 = 81
(-5)2 = (-5)(-5) = 25
-62 = -(6)(6) = -36
(2 • 4)3 = (2 • 4)(2 • 4)(2 • 4) = 8 • 8 • 8 = 512
3 • 42 = 3 • 4 • 4 = 48
Example from today’s homework:
Example from today’s homework:
Product Rule (applies to common bases only)
am • an = am+n
Example
Simplify each of the following expressions.
32 • 34 = 32+4 = 36 = 3 • 3 • 3 • 3 • 3 • 3 = 729
x4 • x5 = x4+5 = x9
z3 • z2 • z5 = z3+2+5 = z10
(3y2)(-4y4) = 3 • y2 • -4 • y4 = (3 • -4)(y2 • y4) = -12y6
Example from today’s homework:
Power Rule
(am)n = amn
Example
Simplify each of the following expressions.
(23)3 = 23•3 = 29 = 512
(x4)2 = x4•2 = x8
Example from today’s homework:
Power of a Product Rule
(ab)n = an • bn
Example
Simplify (5x2y)3 = 53 • (x2)3 • y3 = 125x6 y3
Example from today’s homework:
Power of a Quotient Rule
n
n
a
a
 
   n
b
b
b0
Example
Simplify the following expression.
 p 
 3 
 3r 
2
4

p 

3r 
2 4
3 4

p 

3 r 
2 4
4
3 4
p8

81r 12
(Power of product (Power rule
rule in this step)
in this step)
Example from today’s homework:
Quotient Rule (applies to common bases only)
am
mn

a
an
a0
Example
Simplify the following expression.
4
7
9a b




9
a
b
 
3 5
41
72





3
a
b
    2   3(a )(b )
2
3ab
 3  a  b 
4 7
Group common
bases together
Example from today’s homework:
Zero exponent
a0 = 1, a  0
Note: 00 is undefined.
Example
Simplify each of the following expressions.
50 = 1
(xyz3)0 = x0 • y0 • (z3)0 = 1 • 1 • 1 = 1
-x0 = -(x0) = -1
Example from today’s homework:
Example from today’s homework:
1
Now simplify  
2
Answer = 1
0
You may now
OPEN
your LAPTOPS
and begin working on the
homework assignment.