UNIT 5 EXPONENTS NAME: PERIOD:

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1 NAME: PERIOD: UNIT 5 EXPONENTS Disclaimer: This packet is your notes for all of unit 5. It is expected you will take good notes and work the examples in class with your teacher in pencil. It is expected that you bring your packet to class every day and do not lose it! Should you be absent, it is expected that you get the notes and examples you missed. This packet will be collected and graded out of 50 points during class after the unit 5 test. Notes Examples Neatness Total /20 /20 /10 /50 1 U 5 E x p o n e n t s

2 Exponents Day 1 (Textbook Section 4.2) By the end of the class I will be able to: The base is. It is a factor times. Therefore, the exponent is 2 U 5 E x p o n e n t s

3 The base is. It is a factor times. Therefore, the exponent is The base is. It is a factor times. Therefore, the exponent is The base is. It is a factor times. Therefore, the exponent is Understanding Check: U 5 E x p o n e n t s

4 a b c d Understanding Check: U 5 E x p o n e n t s

5 Exponents Day 2 (Textbook Section 4.2) By the end of the class I will be able to: U 5 E x p o n e n t s

6 Understanding Check: U 5 E x p o n e n t s

7 Exponents and Multiplication Day 3 (Textbook Section 4.7) By the end of the class I will be able to: 7 U 5 E X P O N E N T S

8 Understanding Check: Understanding Check: 8 U 5 E X P O N E N T S

9 Exponents and Multiplication Day 4 (Textbook Section 4.7) By the end of the class I will be able to: 9 U 5 E X P O N E N T S

10 Understanding Check: 10 U 5 E X P O N E N T S

11 MATHEMATICAL REASONING Goldbach's Conjecture NOTE: A conjecture cannot be proved with examples, it can only be tested. A conjecture can be disproved with a counterexample. Even Numbers Odd Numbers Ex. 12= Ex. 15= U 5 E X P O N E N T S

12 Exponents and Multiplication Day 5 (Textbook Section 4.8) By the end of the class I will be able to: In lesson 4.7 you learned that you add exponents when you powers with the same base. For example, = = = What do you think will happen to the exponents when the powers divide? For example, = Expand the numerator and denominator. = Divide common factors = Notice that = = This suggests that when the powers with the same base divide, the exponents. 12 U 5 E X P O N E N T S

13 Step 1: the exponents Step 2: Simplify the exponent Step 3: If your base has numbers, then simplify your final answer. Step 1: the exponents Step 2: Simplify the exponent Step 3: If your base does not have numbers then you are done! 13 U 5 E X P O N E N T S

14 Understanding Check: 14 U 5 E X P O N E N T S

15 Powers of Products Day 6 (Textbook Section 5.9) By the end of the class I will be able to: To raise a product to a power you raise to the power. For example, (ab) 3 means ( ) ( ) ( )= =. 1. Numbers: 2. Number and variable: 3. Variables: 4. Powers: (5 2) 3 (3 t) 4 (x y) 4 (4x 2 ) 3 5. Negative signs outside parenthesis: 6.Negative signs inside parenthesis: -(5x 2 ) 2 a. Raised to an even power: b. Raised to an odd power: (-5x) 2 (-5x) 3 15 U 5 E X P O N E N T S

16 Understanding Check: 16 U 5 E X P O N E N T S

17 Powers of Quotients Day 7 (Textbook Section 5.9) By the end of the class I will be able to: You can use repeated to write a power of a. For example, = = Reading Tip: You read as two thirds to the third power Simplifying a Power of a Quotient a. With a negative sign inside the parenthesis b. With a power inside You have described negative exponents as repeated division. You can use the rule for raising a quotient to a to describe negative exponents as repeated by the multiplicative U 5 E X P O N E N T S

18 Understanding Check: 18 U 5 E X P O N E N T S

19 Scientific Notation Day 8 (Textbook Section 4.9) Date: By the end of the class I will be able to: Do you know this number, 300,000,000 m/sec? Do you recognize this number, kg? Scientific notation is simply a method for and with very or very numbers. It is a short hand method for numbers, which makes them easier to work with. There are two parts to a number in scientific notation. 1. A number between and. 2. A of x is between and. The power has base 10 and exponent. 1. Identifying numbers in scientific notation. Which numbers are in proper scientific notation? x x x x x , 000, x 10 7 Y/N Reason: 19 U 5 EXPONENTS

20 Homework # 41 Due by Tuesday 1/8/13 Research: What is a googol? Write it using scientific notation. 20 U 5 EXPONENTS

21 Scientific Notation Day 9 (Textbook Section 4.9) Date: By the end of the class I will be able to: Scientific Notation of Large Numbers 2. Steps to change a large number from standard form to scientific notation. Ex. Write the number in scientific notation. 1. Put a after the digit in the number. Now you have your number between and. 2. Count the number of the moved. Start at the end of the number. Steps moved:. 3. Rewrite the without the trailing. Multiply it by 10 to the of, since that is the number of moved. Now our number is in scientific notation. The scientific notation of is. Write each number in scientific notation. a) 54,500,000 b) 723, 000 c) 8, 900, 000, Move decimal: 1.Move decimal: 1.Move decimal: 2. Spots moved: 2. Spots moved: 2. Spots moved: 3. Rewrite: 3. Rewrite: 3. Rewrite: 21 U 5 EXPONENTS

22 3. Steps to change a large number from scientific notation to standard form. Ex. Write the number x 10 9 in standard form. 1. Rewrite the number the of ten. 2. Move the decimal spots to the, since that was the in the power of Rewrite the number placing in every blank spot. Now our number is in standard form. The standard form of x 10 9 is:. Write each number in standard form. a) 5.94 x 10 7 b) 1.2 x 10 5 c) 2.75 x Rewrite without power: 1.Rewrite without power: 1.Rewrite without power: 2.Move decimal: 2.Move decimal: 2.Move decimal: 3.Rewrite using zeros: 3.Rewrite using zeros: 3.Rewrite using zeros: 22 U 5 EXPONENTS

23 Understanding Check: Directions: To write the number in scientific notation, first write how many places each decimal must be moved until there is only ONE NUMBER (not zero) in front of the decimal. Then write whether the decimal was moved LEFT or RIGHT. Finally, write the number in scientific notation. NUMBER PLACES MOVED DIRECTION SCIENTIFIC NOTATION 325,000 5 LEFT 3.25 x 10⁵ 89, ,000,000 75,000,000,000 Directions: Write each number in Standard Form. 5.3 x 10³ : 5.3 5, x 10² : 9.03 x 10⁴ : 23 U 5 EXPONENTS

24 Homework # 42 Due by Wednesday 1/9/13: Write each number in standard notation. 1. One light year is 5.88 x miles x x x Writing Math. Explain how to write each number in scientific notation: a) b) x U 5 EXPONENTS

25 Scientific Notation Day 10 (Textbook Section 4.9) Date: By the end of the class I will be able to: Scientific Notation of Small Numbers 4. Steps to change a small number from standard form to scientific notation. In scientific notation you use a negative exponent to write a number between 0 and 1. Ex. Write the number in scientific notation. 1. Put a after the first digit, which is not a, in the number. Now you have your number between and. 2. Count the number of the moved. Spots moved:. 3. Rewrite the without the. Multiply it by 10 to the power of, since that is the number of moved. Now our number is in scientific notation. The scientific notation of is. Understanding Check: Write each number in scientific notation. a) b) c) Move decimal: 1.Move decimal: 1.Move decimal: 2. Spots moved: 2. Spots moved: 2. Spots moved: 3. Rewrite: 3. Rewrite: 3. Rewrite: 25 U 5 EXPONENTS

26 Show your work: 5. Steps to change a small number from scientific notation to standard form. Ex. Write the number x 10 6 in scientific notation. 1. Rewrite the number without the power of ten. 2. Move the decimal spots to the, since that was the in the power of Rewrite the placing in every blank spot. Now our numbers is in standard form. The standard form of x 10 6 is. Understanding Check: Write each number in standard form: a) x 10 8 b) 7.2 x 10 4 c) x Rewrite without power: 1.Rewrite without power: 1.Rewrite without power: 2. Steps moved: 2. Steps moved: 2. Steps moved: 3.Rewrite using zeros: 3.Rewrite using zeros: 3.Rewrite using zeros: 26 U 5 EXPONENTS

27 Show your work: Show your work: 27 U 5 EXPONENTS

28 Homework # 43 Due by Thursday 1/10/13 MIXED PRACTICE 28 U 5 EXPONENTS

29 Scientific Notation Day 11 (Textbook Section 4.9) Date: By the end of the class I will be able to: 29 U 5 EXPONENTS