Grade Scale

1
Grade Scale

• Online Test 1 Results
• Average class score after partial credit
  __________
• Commonly missed questions _________________

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.
2
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 week of class two in-class review sessions
  for the final, each with a homework assignment
• Final Exam Comprehensive, 200 points, during
  evaluation week
• T/Th class (Kokil) 1000 a.m., Tues., May 12
• M/W class (Zick) 800 a.m., Wed, May 13.

3
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.

4

• 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
5
Example from todays homework
6
Example from todays homework
7

• Evaluate the following expressions.
• Find 3x2 when x 5.

3x2 3(5)2
3(5 5)
3 25
75
Find -2x2 when x -1.
-2x2 -2(-1)2
-2(-1 -1)
-2(1)
-2
8
Example from todays homework
9

• Product Rule (applies to common bases only)
• am an amn

Simplify each of the following expressions.
32 34
3 3 3 3 3 3
729
324
36
x4 x5
x45
x9
z3 z2 z5
z325
z10
(3y2)(-4y4)
3 y2 -4 y4
(3 -4)(y2 y4)
-12y6
10
Example from todays homework
11

• Power Rule
• (am)n amn

Simplify each of the following expressions.
(23)3
29
512
233
(x4)2
x8
x42
12
Example from todays homework
13

• Power of a Product Rule
• (ab)n an bn

Simplify (5x2y)3
53 (x2)3 y3
125x6 y3
14
Example from todays homework
15

• Power of a Quotient Rule

Simplify the following expression.
16
Example from todays homework
17

• Quotient Rule (applies to common bases only)

Simplify the following expression.
18
Example from todays homework
19

• Zero exponent
• a0 1, a ? 0
• Note 00 is undefined.

Simplify each of the following expressions. 50
1
(xyz3)0
x0 y0 (z3)0
1 1 1 1
-x0
-(x0)
-1
20
Example from todays homework
21
Example from todays homework
Answer 1
22
You may now OPEN your LAPTOPS and begin working
on the homework assignment.