Ch. 4, Sec 2: Exponents

Warm Up: Find the Product

3 x 3 x 3 x 3 =

-12 x (-12) =

(-4)(-4)(-4)(-4) =

10 · 10 · 10 · 10 · 10 =

Exponents

You can use EXPONENTS to show repeated multiplication.

(Just like multiplication can show repeated addition).

A POWER has two parts:

• A BASE: the factor. (a number or variable)

• And an EXPONENT: the number of times the base (or factor) is multiplied by itself.

97

Base

Exponent

Exponents: Exponential Notation

2 • 2 • 2 • 2 • 2 • 2 = 26

Exponential Notation

Expanded Notation

Exponents…Show me!

1. Exponential Notation.

2. And Value. (The answer).

a. 12

b. 6 x 6

c. –(7 x 7 x 7)

d. (-8)(-8)(-8)(-8)(-8)

Exponential Notation and Answers

• Twelve to the first power.

121, 12

• Six to the second power, or six squared.

62, 6 • 6 = 36

• The opposite of the quantity seven to the fourth power.

-74, - (7 • 7 • 7 • 7)4 = - (2,401) = -2,401

• Negative eight to the fifth power.

(-8)5, (-8)(-8)(-8)(-8)(-8) = -32,768

Writing Exponential Notation

• Remember to include the Negative Sign.

• (-5)(-5)(-5) = (-5)3

• Rewrite the expression using the commutative and associative properties.

• -2 • a • b • a • a =

• -2 • a • a • a • b = -2a3 b

Exponents and Negative Integers

So when you multiply 2 negative numbers… what do you get?

A positive number

When you multiply 3 negative numbers… what do you get?

A negative number

Exponents and Negative Numbers

When you multiply an EVEN number of negative integers, the answer will be positive.

When you multiply an ODD number of negative integers, the answer will be negative.

Word Problem:

• A microscope can magnify a specimen 103 times. How many times is that?

Orders of Operations

1. Work inside the grouping symbols

2. Simplify any terms with exponents.

3. Multiply and divide in order from left to right.

4. Add and subtract in order from left to right.

Example Problem:

• 4(3+2)2 =

1. Grouping Symbols: 3+2 = 5

2. Exponents: 52 = 5 • 5 = 25

3. Multiplying/Dividing: 4 • 25 = 100.

4. Addition/Subtraction?: Nope

• So, 100 is the answer.

Example Problem:• -2x3 + 4y, for x = -2 and y = 3.

• Substitute Variables: -2(-2)3 + 4(3)

1. Grouping Symbols: None

2. Exponents: (-2)3 = (-2)(-2)(-2) = -8

-2(-8)+ 4(3)

3. Multiplication/Division: 16 + 12 = 28

4. Addition/Subtraction: None

• So, 28 is the answer.

Assignment #41:

Page 180: 5 – 31 all.

32 and 33 are extra credit!!!