Transcript Slide 1

8-6
Radical Expressions and Rational Exponents
8-6 LEARNING GOALS
8.6.1 Rewrite radical expressions by using rational exponents.
8.6.2 Simplify and evaluate radical expressions and expressions
containing rational exponents.
The nth root of a real number a can be written as the radical expression:
__________ is the index (plural: indices)
* If the index is left blank it means the index = ________
n
a
__________ is the radicand
Example 1: Finding Real Roots
Find all real roots.
A. sixth roots of 64
B. cube roots of –216
C. fourth roots of –1024
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Radical Expressions and Rational Exponents
Example 2: Writing Expressions in Radical Form
Write the expression
in radical form and simplify.
Method 1 Evaluate the root first.
Method 2 Evaluate the power first.
Use a calculator.
A __________ ____________is an exponent that can be expressed as
.
m
n
For example:

Write the expression in radical form, and simplify.
A. 64⅓
B. 45/2
C. 625¾
Example 3: Writing Expressions by Using Rational Exponents
Write each expression by using rational exponents.
A.
B.
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Radical Expressions and Rational Exponents
Example 4: Simplifying Expressions with Rational Exponents
Simplify each expression. Check with your calculator.
A.
B.
C.
D.
E.
F.
Example 5: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive.
A.
4
81x12
B.

4

D.
5
x

3
3
x7  x2

E.
7
C.
16x4
3
F.
250
3
4
x

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Radical Expressions and Rational Exponents
Example 5: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive.
A.
B.
C.
D.
E.
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Radical Expressions and Rational Exponents
Example 5: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive.
A.
B.
C.
D.
E.
F.
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