Rational exponents
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Transcript of Rational exponents
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How Do We Use Rational Exponents?
• Do Now: Perform the indicated operation and simplify
1.
2.
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nth Rootsnth Roots
An nth root of number a is a number whose nth power is a.
a number whose nth power is a
If the index n is even, then the radicand a must be nonnegative.
is not a real number
n a
4 4
5
16 2, 16
32 2
but
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Square Root of x2
Page 393
xx 2
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Radicals
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Rational Exponents
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Exponent 1/n When n Is Even
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When n Is Even
definedyetnotis44
26464
5625625
10100100
2
1
66
1
44
1
2
1
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Exponent 1/n When n Is Odd
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Exponent 1/n When n Is Odd
2
1
32
1
32
1
32727
32727
55
1
33
1
33
1
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nth Root of Zero
00 n
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Rational Exponents
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Evaluating in Either Order
46488
4288
33 23
2
223
3
2
or
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Negative Rational Exponents
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Evaluating a-m/n
4
1
2
1
8
1
8
18 22
33
23
2
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Rules for Rational Exponents
7-6
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Simplifying
abba
yyy
3
1
2
1
6 66
16
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Simplifying
3
2
2
3
13
11
2
1
113
1
2
1
3
1
2
1
6 66
16
ba
ba
babaabba
yyy
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Simplifying
2
112108
3
2
2
3
3
1
2
1
6 66
16
9 zyx
baabba
yyy
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Multiplying Radicals – Different Indices
32
82222222
3
44 34
3
2
1
4
1
2
1
4
14
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Multiplying RadicalsDifferent Indices
2
1
3
13
44 34
3
2
1
4
1
2
1
4
14
3232
82222222
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Different Indices
6
3
6
2
2
1
3
13
44 34
3
2
1
4
1
2
1
4
14
323232
82222222
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Different Indices
6 36 26
3
6
2
2
1
3
13
44 34
3
2
1
4
1
2
1
4
14
32323232
82222222
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Different Indices
66 36 26
3
6
2
2
1
3
13
44 34
3
2
1
4
1
2
1
4
14
10832323232
82222222
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Rational ExponentsEliminate the root, then the power
23
2
a
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Eliminate the Root, Then the Power
CHECK
a
a
a
a
a
22
8
8
2
2
2
2
3
3
3
2
3
2
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Negative Exponents
11 3
2
r
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Negative ExponentsEliminate the root, then the power
CHECK
rr
r
r
r
r
r
02
11
11
11
11
11
2
2
33
3
2
3
2
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Negative ExponentsEliminate the root, then the power
132 3
2
t
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No SolutionEliminate the root, then the power
132
132
132
132
2
2
33
3
2
3
2
t
t
t
t
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No SolutionEliminate the root, then the power
solutionrealNo
t
t
t
t
132
132
132
132
2
2
33
3
2
3
2
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Strategy for Solving Equations with Exponents and Radicals