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Bittinger
Pre-Algebra, 6th edition
Section 10.2 – Working with Exponents
Tom Atwater
Draft 1
Example from Text:
Exercises from Text: 21, 23, 39, 47, 53, 61
Student: No
Video
Audio
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Section 10.2
[PP 2]
Working with Exponents
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INTRODUCTION:
Hi, my name is Tom. Today we are going
to be working with exponents.
READ Objectives.
Objectives
Use the product rule to multiply
exponential expressions with like
bases.
Use the quotient rule to divide
exponential expressions with like
bases.
Use the power rule to raise powers to
powers.
Raise a product to a power and a
quotient to a power.
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[PP 5]
SAY: We begin with the product rule.
READ Product Rule
Product Rule
For any nonzero number a and any
integers m and n,
am • an = am + n
(To multiply powers with the same base,
keep the base and add the exponents.)
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[PP 6]
SAY: Let’s work two examples.
READ Exercise 23
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Bittinger
Pre-Algebra, 6th edition
Section 10.2 – Working with Exponents
Tom Atwater
Draft 1
Simplify. Assume that no denominator is
0.
a–4 • a9 • a–6
MATH STEPS:
a–4 • a9 • a–6
= a–4 + 9 + (–6)
= a–1
= 1/a
READ Exercise 21
[PP 7]
Simplify. Assume that no denominator is
0.
a 3b 5 ab 9

 
MATH STEPS:
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= (a3a)(b5b9)
= a4b14
SAY: Now we consider the quotient rule.
READ Quotient Rule
Quotient Rule
For any nonzero number a and any
integers m and n,
am
 a m n
n
a
(To divide powers with the same base,
subtract the exponent of the denominator
from the exponent of the numerator.)
FULL SCREEN PRESENTER
[PP 9]
SAY: Here’s an example.
READ Exercise 39
Simplify. Assume that no denominator is
0.
x 4 y12
xy 7
MATH STEPS:
2
Bittinger
Pre-Algebra, 6th edition
Section 10.2 – Working with Exponents
Tom Atwater
Draft 1
x 4 y12
xy 7
 x 4 1 y12  7
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[PP 10]
 x 3 y5
SAY: Let’s turn our attention to the
power rule.
READ Power Rule
Power Rule
For any nonzero number a and any
integers m and n,
a   a
m n
mn
(To raise a power to a power, multiply the
exponents and leave the base unchanged.)
FULL SCREEN PRESENTER
[PP 11]
SAY: Here we work an example.
READ Exercise 47
Simplify. Assume that no denominator is
0.
y 
12 1
MATH STEPS:
y 
12 1
 y12 1
 y 12
1
y12
SAY: Now we consider raising a product
to a power.
READ Raising a Product to a Power
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Raising a Product to a Power
For any nonzero number a and b and any
integer n,
abn  anbn
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Bittinger
Pre-Algebra, 6th edition
Section 10.2 – Working with Exponents
Tom Atwater
Draft 1
(To raise a product to a power, raise each
factor to that power.)
FULL SCREEN PRESENTER
[PP 13]
SAY: Here’s an example.
READ Exercise 53
Simplify. Assume that no denominator is
0.
2a b 
2 5 3
MATH STEPS:
2a b 
 2 a b 
 2  a  b 
2
5 3
1
2
3
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[PP 14]
5 3
2 3
5 3
 8a 6 b15
SAY: Next we discuss raising a quotient
to a power.
READ Raising a Quotient to a Power
Raising a Quotient to a Power
For any nonzero numbers a and b and any
integer n,
n
an
 a

 
b
bn
(To raise a quotient to a power, raise the
numerator to the power and divide by the
denominator to the power.)
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SAY: Let’s work an example.
READ Exercise 61
Simplify. Assume that no denominator is
0.
 x4 
 y 5 
3
MATH STEPS:
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Bittinger
Pre-Algebra, 6th edition
Section 10.2 – Working with Exponents
Tom Atwater
Draft 1
 x4 
 y 5 
3
x 

y 
4 3
5 3
FULL SCREEN PRESENTER
x12
 15
y
CONCLUSION:
Today we learned the product rule,
quotient rule, and power rules . Go back
and review this section before beginning
the exercise set. If you're having any
trouble with the material see your
instructor immediately. Good Luck.
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