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2.2 Properties of Exponents
Objectives
• Evaluate expressions involving exponents.
• Simplify expressions involving exponents.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
2.2 Properties of Exponents
Glossary Terms
base
exponent
power
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
2.2 Properties of Exponents
Rules and Properties
Definition of Integer Exponents
Let a be a real number.
If n is a natural number, then:
an = a  a  a  ...  a, n times.
If a is nonzero, then:
a0 = 1.
If a is a natural number, then:
1
–n
a = n .
a
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
2.2 Properties of Exponents
Rules and Properties
Properties of Exponents
Let a and b be nonzero real numbers.
Let m and n be integers.
Product of Powers
Quotient of Powers
am
(a)m(a)n = am + n
m–n
=
a
n
a
Power of a Power
(am)n = amn
Power of a Product
(ab)n = anbn
Power of an Quotient
a
a n
= n
b
b
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
2.2 Properties of Exponents
Rules and Properties
Definition of Rational Exponents
For all positive real numbers a:
If n is a nonzero integers, then
1
an
= na .
If m and n are integers and n  0, then
m
an
=
1 m
an
=
a
n
m
.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
2.2 Properties of Exponents
Key Skills
Simplify and evaluate expressions by using
the Properties of Exponents.
1
(32)3
a. 4 = 3(2)(3)  4 = 36  3–4 = 36 – 4 = 32 = 9
3
3
Simplify
Definition
Use Power of
a Useofthe Product
Integer of Powers
Power Property
ExponentsProperty
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
2.2 Properties of Exponents
Key Skills
Simplify and evaluate expressions by using
the Properties of Exponents.
b.
xy2
z
3
x3  y(2)(3)
x 3y 6
x3(y2)3
= 3
=
=
3
3
z
z
z
Use Power Simplify
Use Power of
a Quotient of a Power
Property Property
TOC
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.