6.3 Dividing Monomials

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6.3 Dividing Monomials

• CORD Math
• Mrs. Spitz
• Fall 2006

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Okay, for the HW

• Scale How many correct?
• 17-20 20 pointsnot 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!

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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

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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

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Introduction

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

27
243
27
9
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Introduction

• 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

27
243
27
9
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Quotient of Powers

• Now simplify the following

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!
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Example 1

• Simplify the following

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.
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Next note

• Study the two ways shown below to simplify

a3
a3
a a a

a3-3

a3
a a a
a3
a0
1
Zero Exponent For any nonzero number a, a0 1.
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Aha

• Study the two ways shown below to simplify

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
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What does this suggest?

• This examples suggests the following definition

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.
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Example 2

• Simplify the following

-6r3s5




18r-7s5t-2
r3-(-7)s5-5t2
Recall t2
r10s0t2
Subtract the exponents.
r10t2
Remember that s0 1.
-
3
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Example 3

• Simplify the following

(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