Section 2.5: Exponent Laws II Pages/Paula Kelly_files/Grade_9_Math_10_11...Section_2.5_notes_paula_9.3.notebook 4 November 02, 2010 Oct 272:53 PM Section 2.5 - Exponent Laws II Example:

Section_2.5_notes_paula_9.3.notebook

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Section 2.5: Exponent Laws II

Investigation: Copy and complete this table.


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ç ü 212

32 × 32 × 32 × 32 (3)(3) × (3)(3) × (3)(3) × (3)(3) 38

(–4)3 × (–4)3 (–4)(–4)(–4) × (–4)(–4)(–4) (–4)6

(–5)(–5)(–5) × (–5)(–5)(–5) × (–5)(–5)(–5) × (–5)(–5)(–5) × (–5)(–5)(–5)

(–5)3 × (–5)3 × (–5)3 × (–5)3 × (–5)3 (–5)15


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ç ü 23 × 53

(3 × 4) × (3 × 4) 3 × 3 × 4 × 4 32 × 42

(4 × 2) × (4 × 2) × (4 × 2) × (4 × 2) × (4 × 2)

4 × 4 × 4 × 4 × 4 × 2 × 2 × 2 × 2 × 2

45 × 25

5 × 5 × 5 × 5 × 3 × 3 × 3 × 3 (5 × 3) × (5 × 3) × (5 × 3) × (5 × 3) 54 × 34


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November 02, 2010

Oct 272:53 PM

Section 2.5 - Exponent Laws II

Example: Multiply 32 x 32 x 32

Recall that powers can be use to show repeated multiplication.

Since 32 x 32 x 32 is repeated multiplication, this can be written as a power.

So . . . 32 x 32 x 32 = (32)3 Base = 32

Exponent = 3Power = (32)3

Exponent

Base

= 3(2+2+2) = 36

Example: Write as a single power: (32)3.

Answer: (32)3 = (32)(32)(32)= 36 (add the exponents)

Can you get the answer another way? How?

PullPull You could have multiplied the exponents.

The expression (32)3 is called a power of a power.


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3. Exponent Law for a Power of a PowerTo raise a power to a power, we multiply the exponents.

i.e. (am)n = amn

where "a " is any integer except 0 and "m" and "n" are any whole numbers.

(Definition of a power) (Exponent Law for a Power of a Power)

ie: (23)5 OR (23)5 = (23)(23)(23)(23)(23) = 2(3 x 5) = 215 = 215

ie: (32)4 (32)4 = (32)(32)(32)(32) = 38 = 38

Example: Write as a power. Use the exponent law for a Power of a Power.

1. [(-5)3]22. -(23)4

3. [(-2)5]3 4. -(54)2

Pull

Pull(5)3x2

(5)6 (2)3x4212

Pull

Pull

(2)15 Pull

Pull (5)4x2

58

Pull

Pull


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Nov 111:33 AM

Powers of Products

Example. Multiply: (3 x 4)2

Pull

Pull

To multiply (3 x 4)2, write it as a repeated multiplication.

So . . . (3 x 4)2

= (3 x 4)(3 x 4) Remove brackets and group equal factors = 3 x 3 x 4 x 4 Write as power.

= 32 x 42 Evaluate. = 9 x 16

= 144

4. Exponent Law for a Power of a ProductThe power of a product is the product of powers.

i.e. (ab)m = ambm

where "a" and "b" are integers, except 0 and "m" is any whole number.

Example: (2 x 3)4 = 24 x 34


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Example: Write as a product of powers.

A) (1 x 4)4 B) (2 x 5)2

Example: Evaluate.

A) (1 x 4)4 B) (2 x 5)2

Method 2: Follow BEDMAS as before.

=14 x 44 =22 x 52

Method 1: Write as a power of products; then evaluate.

A) (1 x 4)4 B) (2 x 5)2

= 14 x 44

= 1 x 256 = 256

= 22 x 52

= 4 x 25= 100

A) (1 x 4)4 B) (2 x 5)2

= (4)4

= 256= (2 x 5)2

= (10)2

= 100


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Nov 111:49 AM

Product of Powers Evaluate

[(1) x 6]2

[(1) x (4)]3

[2 x (3)]4

Complete the following table.


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Nov 111:52 AM

Power of a Quotient

5 6( (3 5 6( (3

The base of the power is a quotient: 5 . 6

written as repeated multiplication is

5 x x 6

5 6

5 6

= 5 x 5 x 5 6 x 6 x 6

5. Exponent Law for Power of a QuotientThe power of a quotient is the quotient of powers. i.e.

2 3( (4

Evaluate:

= 53 63

where "a" and "b" are integers, except 0 and "n" is any whole number.

Example: Write as a quotient of powers.

= 24 34


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Nov 11:25 PM

Write as a quotient of powers

Evaluate

(5÷8)0 1

Complete the following table.


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Nov 12:28 PM

Write as a quotient of Powers

Evaluate

[(6) ÷ 5]7

[24 ÷ (6)]4


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Nov 12:36 PM

Applying Exponent Laws and Order of Operations

Simplify, then evaluate each

1 2

1. Simplify using laws

2. Evaluate (find the answer)


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Nov 12:43 PM

Try these...

1. 2.

Pull

Pull

Pull

Pull

Text Questions...page 84...4 17, 19

Section 2.5: Exponent Laws II Pages/Paula Kelly_files/Grade_9_Math_10_11...Section_2.5_notes_paula_9.3.notebook 4 November 02, 2010 Oct 272:53 PM Section 2.5 - Exponent Laws II Example:

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