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!!!
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Algebra 2: Section 7.2
Properties of Rational Exponents
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Examples: Simplify
48. 6444 16 4 42 4
Alternate Method
4 62 4 44 22 2 42 4
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Rationalizing Denominator with Rational Exponents
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
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Examples: Simplify
47
9. 8
4
4
7
8 Can’t have a radical in denominator!
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4 3
7
2
4 1
4 1
2
2 Rationalize: now we will have a fourth
power of 2 under the fourth root
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4 4
14
2
4 14
2
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Adding & Subtracting Roots and Rational Exponents
Similar to combining like terms Radical parts must be EXACTLY ALIKE
– Same roots– Same numbers under the radical
May need to simplify radical
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Examples
3 3
4 410. 5 4 3 4
3
42 4
3
4How many 4 are there?
5 3
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Examples
3 311. 81 3Simplify the cube root of 81. May end up with like radicals
3 4 33 33 33 1 33 3 3
3 33 3 332 3
There is a one in front of this radical
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Examples
3 912. 27z
3 93 27 z9
3 3 33 z
33z
Usually easier to simplify variablesIn radicals by changing to rational exponents
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Examples
14 2 213. (16 )g h
1 4 2
2 2 216 g h2 116 g h
24g h
Multiply each exponent by one-half
Usually easier to think of numbers in termsOf radicals instead of rational exponents
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Examples
5
510
14.x
y
5
5
10
5
x
y2
x
y
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Examples
2
3
134
1815.
6
rs
r t
233
1
4
3rs t
r
Simplified 18/6and moved t to numeratorbecause of (-3) exponent
233343r s t
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4r
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Examples
4 9 14416. 12d e f
4 8 1 12 24 12d e e f fFactor out perfect 4th powers.(Powers that are divisible by 4)
4 8 12 1 24 4 12d e f e f
2 3 24 12de f ef
Use product property to rewrite order,so that terms in first radical are thosethat will simplify
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Examples
2
57
17.g
h
25
5 7
g
h
Factor out perfect 5th powers
25
5 5 2
g
h h
25
5 2
g
h h
2 5 35
5 52 3
g h
h h h
2 35
5 5
g h
h h
2 35 g h
h h
2 35
2
g h
h
Can’t have radical in denominator
Rationalize
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Homework
P.411
#43-75 odds
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Homework
P.411#42-74 evens
