8.6.1 Rewrite radical expressions by using rational exponents.

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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 ________ __________ 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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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 . For example
Write the expression in radical form, and
simplify.
A. 64?
B. 45/2
C. 625¾
Example 3 Writing Expressions by Using Rational
Exponents
Write each expression by using rational exponents.
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Example 4 Simplifying Expressions with Rational
Exponents
Simplify each expression. Check with your
calculator.
B.
C.
A.
E.
F.
D.
Example 5 Simplifying Radical Expressions
Simplify each expression. Assume that all
variables are positive. A. B. C. D. E. F.

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Example 5 Simplifying Radical Expressions
Simplify each expression. Assume that all
variables are positive. A. B.
C. D. E.
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Example 5 Simplifying Radical Expressions
Simplify each expression. Assume that all
variables are positive. A. B. C. D. E
. F.
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