Name: ____________________________ Date: ____________________________

CHAPTER 1 NOTES – Powers and Exponent Laws Calendar of Chapter: See the ‘Homework’ link on the webpage

What You’ll Learn: 1.4 – Use powers to represent repeated multiplication & use patterns to understand a power with exponent 0 Scientific Notation – Learn how to put numbers into and take them out of scientific notation 1.5 – Solve problems and perform operations (BEDMAS) involving powers 1.6/1.7 – Explain and apply exponent laws Negative Exponents - To understand and apply negative exponents in evaluating powers Metric Conversions – To learn about and convert metric units When are powers needed in the ‘real world’?

_________________________ 1.4 – Defining a Power___ __________________________ Focus: Use powers to represent repeated multiplication & understand the zero exponent law.

Warmup: Suppose you have a square with length 4cm. a) Draw a picture and calculate the area with proper units. b) How did you calculate the area? c) How could you write a calculation for the area using a power? Name all of the parts of power form. There are 3 ways to Example: write ‘power math’: POWER FORM: REPEATED MULTIPLICATION: STANDARD FORM: Ex1 - Write 16 using each POWER FORM (two ways ): form: REPEATED MULTIPLICATION (two ways ) STANDARD FORM: Ex2 Suppose you have a cube with side length 5cm. Draw the cube & write the volume in power form, as a repeated multiplication, & in standard form with correct units. Ex3: Write as a power & then in standard form: a) 2 x 2 x 2 x 2 x 2 b) (3)(3)(3) c) 7

What do you call a: power with exponent 2? power with exponent 3?

Ex4: Write as a repeated multiplication & in standard form: 46 Ex5 Identify the base of each power, then evaluate the power a) (-3)4 b) -34 Can you write a summary sentence that explains when a negative is part of a base & when it isn’t? Ex6: Get a blank piece of paper from your binder. Fill in the table: How many layers if 5 folds are made? How many layers if 26 folds are made? Ex7 Complete the table Using the pattern developed from the table, what is 100 ? What is the Zero Exponent Law? Ex8 Evaluate each expression: a) 20 b) (-2)0 c) -

FOLDS LAYERS LAYERS IN POWER FORM

0 =

1 =

2 =

3 =

4 =

Power Standard Form

106

105

104

103

102

101

100

To do a power on your calculator, using the exponent button, which looks like: or ^ yx

What is the shortcut for base 10 without a calc?

_____________ Scientific Notation__________________________________ Focus: To understand and apply scientific notation correctly.

Warmup: Write the following as a power of ten: a) 7000 b) 60 What is Scientific Notation? Ex1 Put 80 000 into scientific notation and indicate the coefficient What must be true of the coefficient in order to be in scientific notation? Ex2 Put 22 000 000 into scientific notation Ex3 Put 360 000 000 into scientific notation Ex4 Take a guess: Do you think the light travels to the moon like Watch ‘Act 1’ of the top picture, or the bottom one? ‘the flashlight’ Ask two classmates and record their guess here: What do we need to know to figure this out? Put each into scientific notation with units:

Remember: Scientific notation is just a different way to write the same number!

Ex5 Put 0.0000088 into scientific notation What does a negative exponent mean? Ex6 Put into scientific notation: a) 0.00956 b) 0.000014 How do you put numbers that are in scientific notation back into standard form? Ex7 Put into standard form: a) 2.65 x 10-3 b) 7 x 106 c) 8.3 x 10-5 d) 1 x 100 Ex8 Use your calculator & answer in sci not: a) (3.56 x 10-3)(7.4 x 106)

b) Use your values How long does it take for light to reach from Ex4 to finish the moon? ‘the flashlight’. Was your guess correct? How do you know?

To put 3.56 x 10-3 into your calculator, type in: 3.56 Then, press the: or or Then press the negative button, then 3 (or 3, then the neg button)

EXP EE x10

Time = Distance Speed

___________________1.5 – Order of Operations (DISCOVERY LESSON)________________ Focus: Explain and apply the order of operations with exponents while working in a group.

Group Warmup: 6 x (3 + 2) – 10 2 You win the big prize in the Thrifty’s sweepstakes, but can only claim top prize if you get the skill testing question correct:

6 x (3 + 2) – 10 2 What is the answer? What is the key word for order of operations, and what does each letter mean? Are there any letters that have the same ranking when answering a question? Ex1 – Evaluate by circling each step: a) 33 + 23 b) 3 - 23 c) (3 + 2)3 Ex2 – Evaluate by circling each step: a) [2 x (-3)3 – 6]2 b) 3 + 24 – 3 x (22 – 1)

c) (182 + 50)2 (-5)3 Ex3 – Evaluate to one decimal place

32 142

690

Teacher led method for solving an order of operations question:

6 x (3 + 2) – 10 2

Have your teacher check over all examples to make sure they are correct before moving onto your assignment, which you can also do as a group!

*Note: When you have a long division bar in your question, then do the division LAST.

_________________________1.6 – Exponent Laws ________________________________ Focus: Understand and apply the exponent laws for products and quotients of powers.

Warmup: Complete the table and see if you can find a pattern: Can you describe what the pattern is, so that you do not have to write the middle step? Will the pattern work for the following? 23 x 32 Why or why not? What is the Product Rule? Ex1 Write each expression as a single power: a) 35 x 32 b) 6 x 63 x 64 Let’s investigate how

to find 87 84 Can you describe what the pattern is, so that you don’t have to write the middle step? What is the Quotient Rule?

Product of Powers Product as Repeated

Multiplication Product as

a Power

54 x 52 5x5x5x5 x 5x5 5

35 x 34

23 x 23

46 x 4

Quotient of Powers

Quotient as Repeated Multiplication Quotient as a Power

87 84 ______________________

8

Ex2 Write each expression as a single power:

a) 48 43

b) 4

6

)5(

)5(

Ex3 – Write as a single power:

a) 32 x 34 33 b) (-4)3 x (-4)6 (-4) x (-4)4

Ex4 3

3

2

2

a) Write as a single power b) Simplify using repeated multiplication. c) Why is any base to the zero exponent equal to 1? Ex5 – Evaluate a) 23 x 32 b) (-10)4[(-10)6 (-10)4] – 105

_________________________1.7 – Power Rules___________________________________ Focus: Understand and apply exponent laws for powers of: powers, products, & quotients.

Warmup: Complete the table and see if you can find a pattern: Can you describe what the pattern is, so that you don’t have to write the two middle steps? What is the Power Rule? Ex1 – Simplify as a power: a) (95)6 b) [(-1)3]4 c) –(37)2 Evaluate (3 x 4)5 using BEDMAS Can you find another way to evaluate the question above to get the same answer? What is the Exponent Law for Raising a Product to a Power? Ex2 – Simplify as a power: a) (2 x 3)6 b) [(-8) x 4]2

Power Repeated Multiplication

Expanded Form Power

(23)2 23 x 23 2x2x2 x 2x2x2 2

(42)4

(53)3

[(-3)2]3

Ex3 - Use your newest exponent law to evaluate: a) (2m)3 b) (-3x)2 c) –(2w)4 Evaluate (3 ÷ 4)3 using BEDMAS and a calculator Can you use an exponent law instead, similar to the last exponent law you learned? Test your answer with a calc. What is the Exponent Law for Raising a Quotient to a Power? Ex4 – Simplify as a power

3

3

2

Ex5 – Simplify, then evaluate

a) 2

5

2

x

b) (35 x 3)2 ÷ (33 x 32)2 Can you write a general rule for the 6 exponent laws you’ve learned so far?

Common Mistake: (2 + 4)2 ≠ 22 + 42 The correct answer is (2 + 4)2 = 62 = 36 The operation inside the brackets must be multiplication or division.

_________________________Negative Exponents_________________________________ Focus: To understand and apply negative exponents in evaluating powers

Warmup: Can you write a general rule for the five exponent law you’ve learned so far? Simplify as a single power:

5

3

2

2

Now, expand as a repeated multiplication, cancel, and evaluate. What do you notice? What is an effective way to think about what a negative exponent is? What is the exponent law for negative exponents? Ex1: Simplify, then evaluate. Answer as a fraction in lowest terms: a) 4-2 b) 2-5 c) 76-1 d) (-3)-4

Ex2 – Simplify using exponent laws.

2-5

2-3

Now simplify using expanded form. Ex3: Simplify, then evaluate, as a fraction in lowest terms:

2

2

3

Ex4 – Simplify as a fraction in lowest terms using only exponent laws: a) [(-2)2]-3 x (-2)2

b)

3

572

2

22

4

1

*Note: An answer can never be left in negative exponent form!!

Unit Conversions – Metric

Goal: to learn about and convert metric units

Metric Length Ex1) Ex 2)

What is the base unit & abbrev. for length in metric? _____________________ Base units in metric have no prefix, so their abbreviation is one letter. What are some other units for length in metric? ______ ______ ______ _______ ______ _______ _______ ______ ______ ______ _______ ______ _______ _______ ______ ______ ______ _______ ______ _______ _______ ______ ______ ______ _______ ______ _______ _______ A referent is something (usually handy, or common) used to help estimate or describe a measurement. hectometer: dekametre: metre: centimetre: The beauty of the metric system is that it was made for smooth converting, as it is built on base 10, so you only have to multiply or divide by 10, 100, 1000, etc. What is a quick way to multiply by 10? __________________________ 100? __________________________ 1000? __________________________ What is a quick way to divide by 10? _____________________________ 100? ____________________________ 1000? ____________________________ So we can convert just by jumping the decimal! How many metres is 100 centimetres? ________________ So what happens when you convert from a smaller unit to a larger? Therefore, what should you do if you convert from a larger unit to smaller? Convert a) 75 600 mm to dam b) 2.2 km to m

Ex 3) Ex 4) Ex5)

Convert a) 56.8 m to dm b) 0.43 cm to hm c) 4.19 km to mm d) 9.8 x 101 mm to m The metric system is not just used for measuring length. You can measure many other quantities, and each have their own base unit. However, the metric prefixes (kilo, hector, deka, deci, centi, milli, etc) are all the same. What are some different quantities and their base units: Convert a) 47 dg to dag b) 8 hs to ms c) 5.67 x 10-3 kL to cL d) 9.5 x 103 B to hB Let’s add a few more common prefixes to the list: ____, _____, _____, kilo, hecto, deka, BASE, deci, centi, milli, _____, _____, _____ Convert a) 4.5 x 107 µg to hg b) 7.1 GB to kB