Exponents
6-2
6-2 Rational
Rational
Exponents
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra 1Algebra 1
Holt
McDougal
6-2 Rational Exponents
Warm Up
Simplify each expression.
1.
4.
2.
5.
3.
6.
Holt McDougal Algebra 1
6-2 Rational Exponents
Objective
Evaluate and simplify expressions
containing rational exponents.
Holt McDougal Algebra 1
6-2 Rational Exponents
Recall:
The radical symbol
roots.
is used to indicate
The index is the small number to the left
of the radical symbol that tells which root
to take.
For example
represents a cubic root.
Since 23 = 222 = 8,
Holt McDougal Algebra 1
6-2 Rational Exponents
VOCABULARY:
1. A number raised to the power of
𝒏𝒕𝒉 root of that number.
Examples:
3
𝟏
𝟐
=
𝟏
𝟒
16 =
128
𝟏
𝟕
𝟑
𝟒
=
𝟏𝟔
𝟕
𝟏𝟐𝟖
Holt McDougal Algebra 1
𝟏
𝒏
is equal to the
6-2 Rational Exponents
1
Additional Example 1: Simplifying b
Simplify each expression.
A.
n
1
Use the definition of b n .
=7
B.
1
Use the definition of b n .
=2+3=5
Holt McDougal Algebra 1
6-2 Rational Exponents
Now you try!!!
Simplify each expression.
a.
b.
Holt McDougal Algebra 1
6-2 Rational Exponents
VOCABULARY:
𝒎
𝒏
2. A number raised to the power of is equal to the
𝒏𝒕𝒉 root of that number raised to the m𝒕𝒉 power.
Examples:
8
8
𝟐
𝟑
𝟐
𝟑
𝟑
=
=
𝟑
𝟖
𝟖𝟐
𝟐
= 𝟐𝟐 = 𝟒
=
Holt McDougal Algebra 1
𝟑
𝟔𝟒 = 𝟒
*Both ways
work
6-2 Rational Exponents
Additional Example 2: Simplifying Expressions with
Fractional Exponents
Simplify each expression.
A.
B.
Definition of
= 243
Holt McDougal Algebra 1
= 25
6-2 Rational Exponents
Try these yourself!!!
Simplify each expression.
a.
Holt McDougal Algebra 1
b.
6-2 Rational Exponents
Additional Example 3: Application
Given a cube with surface area S, the volume V
of the cube can be found by using the formula
Find the volume of a cube with
surface area 54 m2.
Substitute 54 for s.
Simplify inside the parentheses.
Definition of
The volume of the cube is 27 m3.
Holt McDougal Algebra 1
6-2 Rational Exponents
Additional Example 4A: Properties of Exponents to
Simplify Expressions
Simplify. All variables represent nonnegative
numbers.
Definition of
•
Power of a Product
Property
Power of a Power Property
Simplify exponents.
Holt McDougal Algebra 1
6-2 Rational Exponents
Additional Example 4B: Properties of Exponents to
Simplify Expressions
Simplify. All variables represent nonnegative
numbers.
•
•
Power of a Product
Property
Simplify exponents.
Product of Powers
Property
Holt McDougal Algebra 1
6-2 Rational Exponents
You try these!!!!
Simplify. All variables represent nonnegative
numbers.
Holt McDougal Algebra 1
6-2 Rational Exponents
HOMEWORK
PG. 401 - 403
# 32-58(evens), 51,
68-70, 84
Holt McDougal Algebra 1