chapter 3 outline powers &...

Chapter 3 Outline Powers & Exponents

This is a tentative schedule. Dates of quizzes and tests may change.

Homework Completion Date Topic Homework Complete In Progress Not Done

Using Exponents to Describe Numbers Powers WS #1

Powers with Negative Bases & Zero Exponents Powers WS #2

Exponent Laws Part 1 Powers WS #3

Quiz: Exponent Basics, Negative Bases, Zero Exponents, Multiplying & Dividing Like Bases Exponent Laws Part 2

Powers WS #4

Mid-Chapter Review Activity Exponent Laws Foldable

Order of Operations with Exponents Powers WS #5

Problem Solving with Exponents Powers WS #6

Chapter 3 Review Practice Test Pg. 122-123

Chapter 3 Test

Ch.3- Powers & Exponents 1

!

Name: __________________________ Math 9

Using Exponents to Describe Numbers

In Math, it is often desirable to write numbers in a short form. One of these ways is by using exponents and powers. What is a Power?

!When an integer, other than 0, can be written as a product of equal factors (numbers you can multiply together to get another number). Example:

5 x 5 x 5 = 53 = 125 Factor or Expanded Form: ______________

Power or Exponential Form: _______

Standard Form: ________

53

Example:

34 is written in power form.

Base: _________ Exponent: __________

Factor or Expanded Form: _________________

Standard Form: ________________

5 is the

3 is the

53 is the


!

This is also used later in algebra:

x5 = x·x·x·x·x where x is the base and 5 is the exponent

Write & Evaluate Powers

a.) Write 2 × 2 × 2 × 2 × 2 in exponential form.

There are _______ factors of 2.

The base is _______ and the exponent is ________.

b.) Evaluate the power- give me the answer in standard form!

Look for your exponent button on your calculator. You will have one of the following:

€

xy

€

^

€

yx

€

x _

Note: The EXP button is not an exponent button!

Powers with Positive Bases

Evaluate each power:

a.) 42 We can say “_______________________”

b.) 23 We can say “_______________________”


!

c.) 36 We can say “_______________________” or

“_____________________________”

Show You Know

1.) Complete the following table:

Factor Form (Products)

Base (Factor)

Exponent Power Form Standard Form (Evaluate)

2 x 2 x 2

9 2

43

100

6 x 6 x 6 x 6

103


!


Name: __________________________ Math 9

Powers with Negative Bases & Zero Exponents

Review When we multiply integers, we use the following rules:

+ × + =

- × - =

When signs are the same, the answer is:

+ × - =

- × + =

When signs are different, the answer is:

We can use these rules when we are multiplying more than two integers. Just multiply two numbers at a time as you move along the problem. Examples (-2) × (-2) × (-2) = _______

(-2) × (-2) × (-2) × (-2) × (-2) × (-2) = _______

Shortcut!

Count the number of negative signs you need to multiply:

! If the number of negative signs is even " _______________

! If the number of negative signs is odd " _______________

Practice

(-5) × (-5) × (-5) × (-5) × (-5) = ________

(-4) × (-4) × (-4) × (-4) = ________


Remember that the exponent only applies to whatever it is directly next to:

! If it is next to a set of brackets, it applies to everything inside the brackets

! If it is next to a number, it only applies to that number

Powers with Negative Bases

Evaluate each power:

a.) (-2)4

b.) -24

c.) (-4)3

d.) –(-5)6


Zero Exponent

Evaluate 30.

You can use a table to determine a pattern in the powers of 3.

Power Value

34

33

32

31

30

So what does this mean?

An exponent of zero will always be equal to _________.

Show You Know

1.) Complete the following table. Describe the pattern that you see as you move up the table (from 50 to 54) or down the table (from 54 to 50).

Power Value

54

53

52

51

50


2.) Explain how (-5)2 and -52 are different and how they are the same.

3.) Evaluate:

a. (-6)2

b. -36

c. (-6)0

d. -30


Name: __________________________ Math 9

Exponent Laws Part 1

Multiplying Powers with the Same Base Write each product of powers as a single power (simplify). Then, evaluate the power (write in standard form).

a.) 23 × 22

Method #1- Repeated Multiplication Method #2- Apply Exponent Law

! Bases are the same, so ___________ the exponents!

b.) (-3)2 × (-3)5

c.) 53 × 35


Dividing Powers with the Same Base Write each quotient of powers as a single power (simplify). Then, evaluate the power (write in standard form).

a.) 26 ÷ 22


! Bases are the same, so ___________ the exponents!

b.)

€

(−5)9

(−5)6

c.) 68 ÷ 28


Show You Know

1.) Evaluate each expression using either repeated multiplication OR exponent laws.

a. 43 × 45

b. (-5)2 × (-5)3

c. 25 ÷ 24

d.

€

(−3)10

(−3)7


Name: __________________________ Math 9

Exponent Laws Part 2

Power of a Power

Write the expression as a single power (simplify). Then, evaluate the power (write in standard form).

a.) (22)3


! _________________ the exponents!

b.) (55)0


Power of a Product

Write the expression as the product of two powers (simplify). Then, evaluate (write in standard form).

a.) [2 × (-3)]4


! Write each factor in the product with _____________________ exponent!

b.) (4 × 9)2


Power of a Quotient

Write the expression as the product of two powers (simplify). Then, evaluate (write in standard form).

a.)

€

34⎛

⎝ ⎜ ⎞

⎠ ⎟ 3


! Write each factor in the quotient with _________________ exponent!

b.)

€

15⎛

⎝ ⎜ ⎞

⎠ ⎟ 5


Key Ideas

! Multiply bases that are the same " ______________________________

! Divide bases that are the same " ______________________________

! Power of a Power " ______________________________

! Power of a Product " ______________________________

! Power of a Quotient " ______________________________

! Zero Exponent " ______________________________

Show You Know

1.) For each expression, simplify then evaluate.

a. (54)2

b. (5 × 4)2

c.

€

25⎛

⎝ ⎜ ⎞

⎠ ⎟ 5

d. [(-3)4]3


Name: __________________________ Math 9

Order of Operations

In previous years, we have learned about order of operations:

B

E

D M

A S

We are going to add in our exponents into our problem solving skills.

Product of a Power

Evaluate:

a.) 3(2)4 b.) -3(-5)2

c.) 5(-4)0 d.) 9(3)5


Evaluate Expressions with Powers

Evaluate:

a.) 42 – 8 ÷ 2 + (-32) b.) -2(-15 – 42) + 4(2 + 3)3

c.) Sheldon was asked to evaluate 128 × 53. What mistake did Sheldon make in his solution? Write the correct solution.

128 × 53

= 6403

= 262 144 000

Show You Know

1.) Evaluate:

a.) 4 × 32 b.) 6(-2)3

c.) (-3 + 6)2 – 4 × 32


Name: __________________________ Math 9

Using Exponents to Solve Problems

Using Formulas to Solve Problems

Write an exponential expression (statement that includes an exponent) to solve each problem:

1.) What is the surface area of a cube with an edge length of 4 cm?

€

SA = 6s2

2.) Find the area of the square attached to the hypotenuse in the diagram.

€

c 2 = a2 + b2

3.) A circle is inscribed in (set into) a square with a side length of 20 cm. What is the area of the shaded region?

Square:

€

A = s2 Circle:

€

A = πr2

5 cm 12 cm

____ cm2


Developing a Formula to Solve a Problem

A dish holds 100 bacteria. It is known that the bacteria will double in number every hour. How many bacteria will be present after each number of hours?

a.) 1 After 1 hour, the bacteria population doubles ______ time.

b.) 5 After 5 hours, the bacteria population doubles ______ times.

c.)

€

n After

€

n hours, the bacteria population doubles ______ times.

Show You Know

1.) What is the surface area of a cube with an edge length of 3 m?


2.) A right triangle has two shorter sides that measure 8 cm and 15 cm. What is the area of a square attached to the hypotenuse?

3.) A type of bacterium is known to triple every hour. There are 50 bacteria to start with. How many will there be after each number of hours?

a. 3

b. 5

c.

€

n

chapter 3 outline powers &...

Documents