Rational Exponents - Morgan Park High School...2013/10/14 · Rational Exponents • You can...
Transcript of Rational Exponents - Morgan Park High School...2013/10/14 · Rational Exponents • You can...
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Rational Exponents
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AAT-A
Date: 12/11/13 SWBAT write and simplify rational exponents in
radical form and vice versa.
Do Now: pg 254 #43-48
HW Requests:
Continue Vocab sheet
In class: pg 261 #4-19
HW: Complete Division of Radicals WS #1-16; pg 261 #21-41 odds
Continue Vocab sheet
In class: pg 261 #4-19
Complete Announcements:
Math Team Cancelled Wed.
Tutoring: Tues. and Thurs. 3-4
"Do not judge me by my successes,
judge me by how many times
I fell down and got back up again.“
Nelson Mandela
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Radicals (also called roots) are
directly related to exponents.
Rational Exponents
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All radicals (roots) can be
written in a different format
without a radical symbol.
Rational Exponents
This different format uses a
rational (fractional) exponent.
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When the exponent of the radicand
(expression under the radical symbol)
is one, the rational exponent form of a
radical looks like this:
Rational Exponents
Remember that the index, n, is a whole number
equal to or greater than 2.
nn aa
1
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Rational Exponents
Examples:
• When a base has a fractional exponent, do not
think of the exponent in the same way as when it is
a whole number.
• When a base has a fractional exponent, the
exponent is telling you that you have a radical
written in a different form.
2
1
66 3
1
3 1111base
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Rational Exponents
For any exponent of the radicand, the
rational exponent form of a radical
looks like this:
n
mm
nn m aaa Power
Root or index
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How do you simplify ?
Rational Exponents
• You can rewrite the expression using a radical.
• Simplify the radical expression, if possible.
• Write your answer in simplest form.
• Reduce the rational exponent, if possible.
2
1
16
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Rational Exponents
Example:
2
1
16 416
3
1
125 51253
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Rational Exponents
Examples:
5
2
32 423222
5
3
5
64 102446455
3
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Rational Exponents
Examples:
No real number solution 2
1
16 16
3
2
216 36621622
3
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Rational Exponents
The basic properties for integer
exponents also hold for rational
exponents as long as the expression
represents a real number.
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Rational Exponents
Example:
What would the answer above be if you
were to write it in radical form? Cont.
6
1
6
3
6
4
2
1
3
2
2
1
3
2
555
5
5
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Rational Exponents
Example:
6
1
6
3
6
4
2
1
3
2
2
1
3
2
555
5
5
6 5
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Rational Exponents
Simplifying radicals – A radical expression is in
simplest form once ALL of the following
conditions have been met.…
• the radicand (expression under the radical symbol) cannot
be written in an exponent form with any factor having an
exponent equal to or larger than the index of the radical;
• there is no fraction under the radical symbol;
• there is no radical in a denominator.
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Rational Exponents
Do you remember the basic Rules of
Exponents that you learned in Roots
and Radicals?
See the next two slides for a quick
review.
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Multiplication Division
b may not be equal to 0.
The Square Root Rules (Properties)
Rational Exponents
b
a
b
ababa
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Multiplication Division
b may not be equal to 0.
The Cube Root Rules (Properties)
Rational Exponents
33
3
b
a
b
a
333 baba
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Rational Exponents
The more general rules for any
radical are as follows …
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Multiplication Division
b may not be equal to 0.
The Rules (Properties)
Rational Exponents
nn
n
b
a
b
a
nnn baba
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Rational Exponents
These same rules in rational exponent
form are as follows …
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Multiplication Division
b may not be equal to 0.
The Rules (Properties)
Rational Exponents
nnn baba111
n
n
n
b
a
b
a1
1
1
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Rational Exponents
In working with radicals, whether in radical
form or in fractional exponent form, simplify
wherever and whenever possible.
What is the process for simplifying radical
expressions?
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Rational Exponents
Examples – Simplifying Radical Expressions:
3 54 3 227 33 227 3 23
5
3
3 6
8
5
5
5
3
25
15
5
15
3 2
3 2
36
6
6
8
3 3
3 2
6
68
6
68 3 2
3
64 3 2
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This different format uses a
rational (fractional) exponent.
Rational Exponents