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...
Rational Exponents
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
Radicals (also called roots) are
directly related to exponents.
Rational Exponents
All radicals (roots) can be
written in a different format
without a radical symbol.
Rational Exponents
This different format uses a
rational (fractional) exponent.
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
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
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
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
Rational Exponents
Example:
2
1
16 416
3
1
125 51253
Rational Exponents
Examples:
5
2
32 423222
5
3
5
64 102446455
3
Rational Exponents
Examples:
No real number solution 2
1
16 16
3
2
216 36621622
3
Rational Exponents
The basic properties for integer
exponents also hold for rational
exponents as long as the expression
represents a real number.
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
Rational Exponents
Example:
6
1
6
3
6
4
2
1
3
2
2
1
3
2
555
5
5
6 5
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.
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.
Multiplication Division
b may not be equal to 0.
The Square Root Rules (Properties)
Rational Exponents
b
a
b
ababa
Multiplication Division
b may not be equal to 0.
The Cube Root Rules (Properties)
Rational Exponents
33
3
b
a
b
a
333 baba
Rational Exponents
The more general rules for any
radical are as follows …
Multiplication Division
b may not be equal to 0.
The Rules (Properties)
Rational Exponents
nn
n
b
a
b
a
nnn baba
Rational Exponents
These same rules in rational exponent
form are as follows …
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
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?
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
This different format uses a
rational (fractional) exponent.
Rational Exponents