CHAPTER 6
6-2 RATIONAL EXPONENTS
OBJECTIVES
• Evaluate and simplify expressions containing
rational exponents.
INDEX
• Recall that the radical symbol
is used to
indicate roots. 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,
WRITING RATIONAL EXPRESSIONS
• Another way to write nth roots is by using
fractional exponents. For example, for b >1,
suppose
• Solution:
•
•
Square both sides
• b1 = b2k
If bm = bn, then m = n.
• 1 = 2k
•
So for all b > 1,
DEFINITION OF RATIONAL EXPRESSION
EXAMPLE#1 SIMPLIFYING
• A)
• Solution:
• B)
• Solution:
=7
=2+3=5
EXAMPLE#1A
•
•
•
•
Simplify each expression.
A)
Solution:
=3
B)
• Solution:
= 11 + 4
= 15
RATIONAL EXPONENTS
• A fractional exponent can have a numerator other
than 1, as in the expression . You can write the
exponent as a product in two different ways.
•P
•
Power of a Power
Property
• Or
• Definiti
Definition of 1/b
DEFINITION
EXAMPLE 2: SIMPLIFYING
EXPRESSIONS WITH FRACTIONAL
EXPONENTS
• Simplify each expression.
• A)
• Solution:
• B)
• Solution:
= 3
5
= 243
= 5 2 = 25
EXAMPLE#2A
• Simplify each expression.
• A)
• Solution:
• B)
• Solution:
•
=8
= (1)3 = 1
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
SOLUTION:
Substitute 54 for s.
Simplify inside the parentheses.
The volume of the cube is 27 m3.
SIGN OF RATIONAL EXPRESSIONS
• Remember that
always indicates a
nonnegative square root. When you simplify
variable expressions that contain , such as
the answer cannot be negative. But x may be
negative. Therefore you simplify
as |x| to
ensure the answer is nonnegative.
Additional Example 4: Properties of Exponents to
Simplify Expressions
• Simplify. All variables represent nonnegative
numbers.
• Solution:
•
EXAMPLE 4A
• Simplify. All variables represent nonnegative
numbers.
• Solution:
EXAMPLE 4B
• Simplify. All variables represent nonnegative
numbers.
• Solution:
= xy
STUDENT GUIDED PRACTICE
• Do even problems 2-25 in your book page 401
HOMEWORK
• Do even problems in your book 31-54 in your book
page 401
CLOSURE
• Today we learned about rational expressions
• Next class we are going to learn about polynomials