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9-2 PPT

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WRITING RADICALS IN RATIONAL
FORM
Rational Exponents
1
DEFINITIONS
a
m
EXPONENT
BASE
Base: The term/variable of which is being raised
upon
Exponent: The term/variable is raised by a term. AKA
Power
9/23/2014 11:16 AM
Rational Exponents
2
NTH ROOT RULE
a
m /n
пЂЅ
пЂЁ aпЂ©
m
n
• M is the power (exponent)
• N is the root
• A is the base
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Rational Exponents
3
RULES
Another way of writing 25 is 251/2.
2 5 is written in radical expression form.
251/2 is written in rational exponent form.
4
EXAMPLE 1
a
m /n
пЂЅ
пЂЁ aпЂ©
m
n
Evaluate 43/2 in radical form and simplify.
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- Rational Exponents
5
EXAMPLE 1
a
m /n
пЂЅ
пЂЁ aпЂ©
m
n
Evaluate 43/2 in radical form and simplify.
4
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3/2
пЂЅ
пЂЁ 4пЂ©
Rational Exponents
3
6
EXAMPLE 2
Evaluate 41/2 in radical form
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10.2 - Rational Exponents
7
YOUR TURN
Evaluate (–27)2/3 in radical form
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10.2 - Rational Exponents
8
EXAMPLE 3
a
пЂЅ
m /n
пЂЁ aпЂ©
m
n
Evaluate –274/3 in radical form
Hint: Remember, the negative is OUTSIDE of the base
пЂ­
пЂЁ
3
27
пЂ©
4
9
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10.2 - Rational Exponents
EXAMPLE 4
Evaluate пЂЁ 4 x пЂ­ 1 пЂ© in radical form and simplify.
3/5
5
пЂЁ 4 x пЂ­ 1пЂ©
3
10
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10.2 - Rational Exponents
4
рќ‘Ћ
3рќ‘Ћ10 рќ‘Џ 6
31/4 рќ‘Ћ5/2 рќ‘Џ 3/2
1/2 3/4 3/8
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рќ‘Џ
рќ‘ђ
10.2 - Rational Exponents
8
рќ‘Ћ4 рќ‘Џ6 рќ‘ђ 3
11
PROPERTIES OF EXPONENTS
Product of a Power:
a
( ab )
Negative Power Property:
Quotient Power Property:
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пѓ—a пЂЅ a
n
mпЂ«n
(a ) пЂЅ a
Power of a Power:
Power of a Product:
m
10.2 - Rational Exponents
m пѓ—n
m
n
m
пЂЅa b
m
(a )
a
m
a
n
пЂ­n
пЂЅ
1
a
пЂЅa
m
n
m пЂ­n
12
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