7­6
Rational Exponents
1. Write expressions with rational exponents in radical form
2. Write expressions in radical form with rational exponents
3. Evaluate and Simplify expressions in both exponential and radical form
1
A rational exponent is an exponent that is expressed as a ratio or fraction.
For any real number b and any positive integer n, 1
b
n
exponential form
=
n
b
radical form
REMEMBER THIS PHRASE:
POWER
ROOT
LIKEWISE...
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POWER
ROOT
For example...
We can change expressions from exponential form to radical form and vice versa
3
and
3
We can also evaluate expressions
with rational exponents 3
POWER
ROOT
Here are some more examples of how rational exponents work...
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POWER
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Okay... your turn!
EXAMPLES
Write in exponential form
b
6
x
4
Note: A radical expression is in simplest form when the index is as small as possible
5
POWER
ROOT
EXAMPLES
Write in radical form:
Note: A radical expression is in simplest form when the radicand contains no factors that
are nth powers of an integer or polynomial
6
POWER
ROOT
EXAMPLES
Evaluate each expression
7
All of the properties of exponents we learned in Chapter 6 still apply to expressions with rational exponents.
RULES OF EXPONENTS
when you multıply lıke bases, you __________the exponents
when you dıvıde lıke bases, you _______________the exponents
when you take a power to a power, you________________ the
exponents
no negatıve exponents (move them to make them posıtıve)
no fractıonal exponents ın denomınator/ no radıcals ın
denomınator
8
Simplify each expression
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Simplify each expression
10
Simplify each expression
4
36b
5
48
5
3
2
11
Simplify each expression
k
256
3
2
mn
12
Homework
WS 7.6
Do not use a calculator!
POWER
ROOT
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