Transcript Algebra 2:

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1
Write out on the board how to do them using
radicals!!! The PP has how to solve using
powers….you show how to use radicals!!!
Algebra 2: Section 7.2
Properties of Rational
Exponents
2
Examples: Simplify
4
8. 64
4
16  4  2 4
4
4
Alternate Method
4
3
2  2  2
6
4
4
4
2
2 4
4
Rationalizing Denominator with
Rational Exponents
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4
Goal: Create an exponent in denominator
that is a whole number
Base that you multiply top and bottom of
fraction by must have exponent that adds to
a whole number in the denominator
Examples: Simplify
9.
4
7 47
 4
8
8


5
4
4
4
4
7
2
3
Can’t have a radical in denominator!

4
4
1
2
1
2
4
14

4
2
2
14
Rationalize: now we will have a fourth
power of 2 under the fourth root
Adding & Subtracting Roots and
Rational Exponents
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Similar to combining like terms
Radical parts must be EXACTLY ALIKE
–
–
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Same roots
Same numbers under the radical
May need to simplify radical
Examples
3


   
10. 5  4   3  4   2  4 4 
 
   
3
4
3
4
5
3
3
4
How many 4 are there?
7
Examples
11.
3
3
81  3
3
3
3 33
4
3  3  3
3
3
1
3
3 3 3
3
8
Simplify the cube root of 81.
May end up with like radicals
3
23 3
There is a one in front of this radical
Examples
12. 3 27z 9
3
3
27 z
3
3 z
3
3z
9
9
3
9
3
Usually easier to simplify variables
In radicals by changing to rational exponents
Examples
1
2 2
13. (16 g 4 h )
1
2
4
2
16 g h
2
2
16  g h
2 1
2
4g h
10
Multiply each exponent by one-half
Usually easier to think of numbers in terms
Of radicals instead of rational exponents
Examples
14.
5
x5
10
y
x
y
11
5
5
10
5
x
 2
y
Examples
15.
18rs
2
3
1
4 3
6r t
2
3 3
3rs t
r
12
1
4
Simplified 18/6
and moved t to numerator
because of (-3) exponent
3
4
2
3 3
 3r s t
r
1
1
4
Examples
4 9
4
16. 12d e f
4
4
14
12d 4 e8e1 f 12 f 2
4 8
d e f
12
 12e f
4
1
de 2 f 3 4 12ef 2
13
Factor out perfect 4th powers.
(Powers that are divisible by 4)
2
Use product property to rewrite order,
so that terms in first radical are those
that will simplify
Examples
2
17.
5
g
h7
Can’t have
radical in
denominator
Factor out
perfect 5th
powers

5
5
g
2
h
7

5
5
g2
5 2

hh
g2
5
5
h h
2
Rationalize
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14
5
g
2
h 5 h2

5
5
h
3
h3

5
g 2 h3
5
h h
5
5
2 3
g h


hh
5
g 2 h3
2
h
Homework
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P.411
#43-75 odds
Homework
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P.411
#42-74 evens