Abstract image of a woman sitting on books and studying on a laptop

Integrated 3.8

Download as ZIP, PDF
S
sfulkerson

Here are the steps to solve these examples using the laws of exponents: 1. (−2)3 × (−2)4 = (−2)3+4 by the product rule = (−2)7 2. (3t)2 × (3t) = (3t)2+1 by the product rule = (3t)3 So the answers are: 1. (−2)7 2. (3t)3

TechnologyEducation
1 of 55
Download to read offline
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659 2 2.8561⋅10
WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659 2 −2 2.8561⋅10 8.659 ⋅10 €
3.8 LAWS OF EXPONENTS Essential Question: What are the laws of exponents?
PRODUCT RULE: m n m +n a ⋅a =a €
PRODUCT RULE: m n m +n a ⋅a =a What does this mean? €
PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = € €
PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = € € €
PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = 8 5 € € € €
PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = 8 5 € €If you are MULTIPLYING €the SAME BASE have € then ADD THE EXPONENTS
QUOTIENT RULE: m n m−n a ÷a =a €
QUOTIENT RULE: m n m−n a ÷a =a What does this mean? €
QUOTIENT RULE: m n m−n a ÷a =a What does this mean? 5 ÷ 5 = 3 2 € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 € € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 5⋅ 5 5⋅ 5 € € € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 =5 5⋅ 5 5⋅ 5 € € € €
QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 =5 5⋅ 5 5⋅ 5 € € If you are DIVIDING € € have the SAME BASE then SUBTRACT THE EXPONENTS
POWER RULE: m n m⋅ n (a ) = a €
POWER RULE: m n m⋅ n (a ) = a What does this mean? €
POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = € €
POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = € € €
POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = 8 6 € € € €
POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = 8 6 € If you have a€ POWER to a POWER € € then MULTIPLY THE EXPONENTS
EXAMPLES: 1. (−2) 3 ⋅ (−2) = 4 2. (3t) 2 ⋅ (3t) = 4 3. (2m) ÷ (2m) = 9 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = 2. (3t) 2 ⋅ (3t) = 4 €9 3. (2m) ÷ (2m) = 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = 4 €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 2 € 4 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 2 € 4 = € 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = 4. ((3k) ) 2 € 4 = € € 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. ((3k) ) 2 € 4 = € € € 5. ((−2) 3 ) 4 = 6. (−4) ÷ (−4) = 8 3
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = € € 5. ((−2) 3 ) 4 = € 8 6. 3 (−4) ÷ (−4) =
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € € 5. ((−2) 3 ) 4 = € 8 €3 6. (−4) ÷ (−4) =
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 ((−2) 3 ) = € 8 €3 6. (−4) ÷ (−4) = €
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. (−4) ÷ (−4) = € €
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. 8−3 (−4) ÷ (−4) = (−4) = € €
EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. 8−3 (−4) ÷ (−4) = (−4) = (−4) 5 € €
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25 incorrect
SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25 incorrect 1 / 25
HOMEWORK: page 138-139 #16-51

More Related Content

ZIP
FST 1.2
sfulkerson
 
ZIP
FST 1..3
sfulkerson
 
ZIP
AA 1.7
sfulkerson
 
ZIP
AA 1.2
sfulkerson
 
ZIP
AA 3.2
sfulkerson
 
PDF
AA 3.4
sfulkerson
 
PPTX
2.2.2 the graph of a function
Northside ISD
 
PDF
AA 2.3 & 2.9
sfulkerson
 
FST 1.2
sfulkerson
 
FST 1..3
sfulkerson
 
AA 1.7
sfulkerson
 
AA 1.2
sfulkerson
 
AA 3.2
sfulkerson
 
AA 3.4
sfulkerson
 
2.2.2 the graph of a function
Northside ISD
 
AA 2.3 & 2.9
sfulkerson
 

Recently uploaded (20)

PDF
Introduction to MCP and A2A Protocols: Enabling Agent Communication
Maxim Salnikov
 
PDF
Connector Corner: Transform Unstructured Documents with Agentic Automation
DianaGray10
 
PDF
A symptom-driven medical diagnosis support model based on machine learning te...
IAESIJAI
 
PPTX
Module 1 Introduction to Web Programming .pptx
kamleshkc191
 
PPTX
Internet of Everything -Basic concepts details
sendilkumar66
 
PDF
The-2025-Engineering-Revolution-AI-Quality-and-DevOps-Convergence.pdf
Kalilur Rahman
 
PDF
SaaS reusability assessment using machine learning techniques
IAESIJAI
 
PDF
Human Computer Interaction Miterm Lesson
JasperGarcia9
 
PDF
5-Ways-AI-is-Revolutionizing-Telecom-Quality-Engineering.pdf
Kalilur Rahman
 
PDF
Aug23rd - Mulesoft Community Workshop - Hyd, India.pdf
Ravi Tamada
 
PDF
Lung cancer patients survival prediction using outlier detection and optimize...
IAESIJAI
 
PDF
Dell Pro Micro: Speed customer interactions, patient processing, and learning...
Principled Technologies
 
PDF
giants, standing on the shoulders of - by Daniel Stenberg
Daniel Stenberg
 
PDF
A hybrid framework for wild animal classification using fine-tuned DenseNet12...
IAESIJAI
 
PDF
NewMind AI Weekly Chronicles – August ’25 Week IV
NewMind AI
 
PDF
“The Future of Visual AI: Efficient Multimodal Intelligence,” a Keynote Prese...
Edge AI and Vision Alliance
 
PDF
Data Virtualization in Action: Scaling APIs and Apps with FME
Safe Software
 
PDF
The-Future-of-Automotive-Quality-is-Here-AI-Driven-Engineering.pdf
Kalilur Rahman
 
PPTX
Presentation - Principles of Instructional Design.pptx
Ntokozo Mhlongo
 
PDF
LMS bot: enhanced learning management systems for improved student learning e...
IAESIJAI
 
Introduction to MCP and A2A Protocols: Enabling Agent Communication
Maxim Salnikov
 
Connector Corner: Transform Unstructured Documents with Agentic Automation
DianaGray10
 
A symptom-driven medical diagnosis support model based on machine learning te...
IAESIJAI
 
Module 1 Introduction to Web Programming .pptx
kamleshkc191
 
Internet of Everything -Basic concepts details
sendilkumar66
 
The-2025-Engineering-Revolution-AI-Quality-and-DevOps-Convergence.pdf
Kalilur Rahman
 
SaaS reusability assessment using machine learning techniques
IAESIJAI
 
Human Computer Interaction Miterm Lesson
JasperGarcia9
 
5-Ways-AI-is-Revolutionizing-Telecom-Quality-Engineering.pdf
Kalilur Rahman
 
Aug23rd - Mulesoft Community Workshop - Hyd, India.pdf
Ravi Tamada
 
Lung cancer patients survival prediction using outlier detection and optimize...
IAESIJAI
 
Dell Pro Micro: Speed customer interactions, patient processing, and learning...
Principled Technologies
 
giants, standing on the shoulders of - by Daniel Stenberg
Daniel Stenberg
 
A hybrid framework for wild animal classification using fine-tuned DenseNet12...
IAESIJAI
 
NewMind AI Weekly Chronicles – August ’25 Week IV
NewMind AI
 
“The Future of Visual AI: Efficient Multimodal Intelligence,” a Keynote Prese...
Edge AI and Vision Alliance
 
Data Virtualization in Action: Scaling APIs and Apps with FME
Safe Software
 
The-Future-of-Automotive-Quality-is-Here-AI-Driven-Engineering.pdf
Kalilur Rahman
 
Presentation - Principles of Instructional Design.pptx
Ntokozo Mhlongo
 
LMS bot: enhanced learning management systems for improved student learning e...
IAESIJAI
 
Ad

Featured (20)

PDF
2024 Trend Updates: What Really Works In SEO & Content Marketing
Search Engine Journal
 
PDF
Storytelling For The Web: Integrate Storytelling in your Design Process
Chiara Aliotta
 
PDF
Artificial Intelligence, Data and Competition – SCHREPEL – June 2024 OECD dis...
OECD Directorate for Financial and Enterprise Affairs
 
PDF
How to Leverage AI to Boost Employee Wellness - Lydia Di Francesco - SocialHR...
SocialHRCamp
 
PDF
2024 State of Marketing Report – by Hubspot
Marius Sescu
 
PDF
Everything You Need To Know About ChatGPT
Expeed Software
 
PDF
Product Design Trends in 2024 | Teenage Engineerings
Pixeldarts
 
PDF
How Race, Age and Gender Shape Attitudes Towards Mental Health
ThinkNow
 
PDF
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
marketingartwork
 
PDF
Skeleton Culture Code
Skeleton Technologies
 
PDF
PEPSICO Presentation to CAGNY Conference Feb 2024
Neil Kimberley
 
PDF
Content Methodology: A Best Practices Report (Webinar)
contently
 
PPTX
How to Prepare For a Successful Job Search for 2024
Albert Qian
 
PDF
Social Media Marketing Trends 2024 // The Global Indie Insights
Kurio // The Social Media Age(ncy)
 
PDF
Trends In Paid Search: Navigating The Digital Landscape In 2024
Search Engine Journal
 
PDF
5 Public speaking tips from TED - Visualized summary
SpeakerHub
 
PDF
ChatGPT and the Future of Work - Clark Boyd
Clark Boyd
 
PDF
Getting into the tech field. what next
Tessa Mero
 
PDF
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Lily Ray
 
PDF
How to have difficult conversations
Rajiv Jayarajah, MAppComm, ACC
 
2024 Trend Updates: What Really Works In SEO & Content Marketing
Search Engine Journal
 
Storytelling For The Web: Integrate Storytelling in your Design Process
Chiara Aliotta
 
Artificial Intelligence, Data and Competition – SCHREPEL – June 2024 OECD dis...
OECD Directorate for Financial and Enterprise Affairs
 
How to Leverage AI to Boost Employee Wellness - Lydia Di Francesco - SocialHR...
SocialHRCamp
 
2024 State of Marketing Report – by Hubspot
Marius Sescu
 
Everything You Need To Know About ChatGPT
Expeed Software
 
Product Design Trends in 2024 | Teenage Engineerings
Pixeldarts
 
How Race, Age and Gender Shape Attitudes Towards Mental Health
ThinkNow
 
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
marketingartwork
 
Skeleton Culture Code
Skeleton Technologies
 
PEPSICO Presentation to CAGNY Conference Feb 2024
Neil Kimberley
 
Content Methodology: A Best Practices Report (Webinar)
contently
 
How to Prepare For a Successful Job Search for 2024
Albert Qian
 
Social Media Marketing Trends 2024 // The Global Indie Insights
Kurio // The Social Media Age(ncy)
 
Trends In Paid Search: Navigating The Digital Landscape In 2024
Search Engine Journal
 
5 Public speaking tips from TED - Visualized summary
SpeakerHub
 
ChatGPT and the Future of Work - Clark Boyd
Clark Boyd
 
Getting into the tech field. what next
Tessa Mero
 
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Lily Ray
 
How to have difficult conversations
Rajiv Jayarajah, MAppComm, ACC
 
Ad

Integrated 3.8

  • 1. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
  • 2. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
  • 3. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
  • 4. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
  • 5. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
  • 6. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
  • 7. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659 2 2.8561⋅10
  • 8. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659 2 −2 2.8561⋅10 8.659 ⋅10 €
  • 9. 3.8 LAWS OF EXPONENTS Essential Question: What are the laws of exponents?
  • 10. PRODUCT RULE: m n m +n a ⋅a =a €
  • 11. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? €
  • 12. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = € €
  • 13. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = € € €
  • 14. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = 8 5 € € € €
  • 15. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = 8 5 € €If you are MULTIPLYING €the SAME BASE have € then ADD THE EXPONENTS
  • 16. QUOTIENT RULE: m n m−n a ÷a =a €
  • 17. QUOTIENT RULE: m n m−n a ÷a =a What does this mean? €
  • 18. QUOTIENT RULE: m n m−n a ÷a =a What does this mean? 5 ÷ 5 = 3 2 € €
  • 19. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 € € €
  • 20. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
  • 21. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
  • 22. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
  • 23. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 5⋅ 5 5⋅ 5 € € € €
  • 24. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 =5 5⋅ 5 5⋅ 5 € € € €
  • 25. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 =5 5⋅ 5 5⋅ 5 € € If you are DIVIDING € € have the SAME BASE then SUBTRACT THE EXPONENTS
  • 26. POWER RULE: m n m⋅ n (a ) = a €
  • 27. POWER RULE: m n m⋅ n (a ) = a What does this mean? €
  • 28. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = € €
  • 29. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = € € €
  • 30. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = 8 6 € € € €
  • 31. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = 8 6 € If you have a€ POWER to a POWER € € then MULTIPLY THE EXPONENTS
  • 32. EXAMPLES: 1. (−2) 3 ⋅ (−2) = 4 2. (3t) 2 ⋅ (3t) = 4 3. (2m) ÷ (2m) = 9 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
  • 33. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = 2. (3t) 2 ⋅ (3t) = 4 €9 3. (2m) ÷ (2m) = 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
  • 34. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = 4 €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
  • 35. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 2 € 4 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
  • 36. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 2 € 4 = € 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
  • 37. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = 4. ((3k) ) 2 € 4 = € € 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
  • 38. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. ((3k) ) 2 € 4 = € € € 5. ((−2) 3 ) 4 = 6. (−4) ÷ (−4) = 8 3
  • 39. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = € € 5. ((−2) 3 ) 4 = € 8 6. 3 (−4) ÷ (−4) =
  • 40. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € € 5. ((−2) 3 ) 4 = € 8 €3 6. (−4) ÷ (−4) =
  • 41. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 ((−2) 3 ) = € 8 €3 6. (−4) ÷ (−4) = €
  • 42. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. (−4) ÷ (−4) = € €
  • 43. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. 8−3 (−4) ÷ (−4) = (−4) = € €
  • 44. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. 8−3 (−4) ÷ (−4) = (−4) = (−4) 5 € €
  • 45. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
  • 46. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
  • 47. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
  • 48. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
  • 49. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
  • 50. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 6. 5-2 = -25
  • 51. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 6. 5-2 = -25
  • 52. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25
  • 53. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25 incorrect
  • 54. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25 incorrect 1 / 25