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6.3 Dividing Monomials. CORD Math Mrs. Spitz Fall 2006. Okay, for the HW. Scale: How many correct? 17-20 – 20 points—not bad – you have it! 12-16 – 15 points – You need some practice 7-11 – 10 points. You need some help. Practice some more – rework the problems missed

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6.3 Dividing Monomials

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6 3 dividing monomials l.jpg

6.3 Dividing Monomials

CORD Math

Mrs. Spitz

Fall 2006


Okay for the hw l.jpg

Okay, for the HW

  • Scale: How many correct?

    • 17-20 – 20 points—not bad – you have it!

    • 12-16 – 15 points – You need some practice

    • 7-11 – 10 points. You need some help. Practice some more – rework the problems missed

    • 6 and below – you need some significant help in order to complete this. Take the worksheet and have mom or dad sign it. Rework problems

  • Turn it in for credit in the box! Record your scores

  • Quiz after 6.3 is graded next time we meet!


Standard objective l.jpg

Standard/Objective

  • Standard: Students will understand algebraic concepts and applications

  • Objectives:

    • Students will simplify expressions involving quotients of monomials, and

    • Simplify expressions containing negative exponents


Assignment l.jpg

Assignment

  • WS 6.3

  • Quiz – end of the 6.2 – 20 minutes

  • Mid-chapter Test after 6.4

  • Quiz after 6.6

  • Test after 6.9 – short answer – show all work


Introduction l.jpg

Consider each of the following quotients. Each number can be expressed as a power of 3.

81

35

27

34

33

= 32

= 9

= 31

= 33

= 3

27

3

32

31

33

Introduction

27

243

= 27

9


Introduction6 l.jpg

Once again, look for a pattern in the quotients shown. If you consider only the exponents, you may notice that

4 – 3 = 1, 3 – 1 = 2, and 5 – 2 = 3

81

35

27

34

33

= 32

= 9

= 31

= 33

= 3

27

3

32

31

33

Introduction

27

243

= 27

9


Quotient of powers l.jpg

Now simplify the following:

b5

=

b2

Quotient of Powers

Quotient of Powers:

For all integers m and n, and any nonzero number a,

b ≠ 0

am

= am-n

an

b · b · b · b · b

= b · b · b

b · b

= b3

These examples suggest that to divide powers with the same base, you can subtract the exponents!


Example 1 l.jpg

Simplify the following:

a4

b3

a1

b2

Example 1

a4b3

=

ab2

= a4-1b3-2

Group the powers that have the same base.

= a3b1

Subtract the exponents by the quotient of powers property.

= a3b

Recall that b1 = b.


Next note l.jpg

Study the two ways shown below to simplify

a3

a3

Next note:

a3

a3

a · a · a

=

a3-3

=

a3

a · a · a

a3

= a0

= 1

Zero Exponent:

For any nonzero number a, a0 = 1.


Slide10 l.jpg

Study the two ways shown below to simplify

k2

k2

k7

k7

Aha:

k2

k · k

k2

=

k2-7

=

k7

k7

k · k · k · k · k · k · k

= k-5

1

=

k · k · k · k · k

Since cannot have two

different values, we can conclude that k-5

1

=

k5

1

=

k5


What does this suggest l.jpg

This examples suggests the following definition:

What does this suggest?

Negative Exponents:

For any nonzero number a and any integer n, a-n

1

=

an

To simplify an expression involving monomials, write an equivalent expression that has positive exponents and no powers of powers. Also, each base should appear only once and all fractions should be in simplest form.


Example 2 l.jpg

Simplify the following:

s5

-1

-6

r3

1

-1

1

t-2

3

r-7

s5

t-2

3

18

Example 2

-6r3s5

=

·

·

·

18r-7s5t-2

= r3-(-7)s5-5t2

Recall = t2

= r10s0t2

Subtract the exponents.

= r10t2

Remember that s0 = 1.

-

3


Example 3 l.jpg

Simplify the following:

4-2

a2

=

·

22

a8

1

1

= 64a6

= 43a6

Example 3

(4a-1)-2

Power of a product property

(2a4)2

4-2

a2

=

Simplify

4a8

= 4-2-1a2-8

Subtract the exponents

= 4-3a-6

Definition of negative exponents

Simplify


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