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Rational Exponents10.210.2
1. Evaluate rational exponents.2. Write radicals as expressions raised to rational
exponents.3. Simplify expressions with rational number exponents
using the rules of exponents.4. Use rational exponents to simplify radical expressions.
2505
25251
5
12
1
Integer ExponentsInteger Exponents
25
32 xx 5x
32x
432ba 128ba
6x
Integer ExponentsInteger Exponents
2/116 2/124
Rational ExponentsRational Exponents
2
12
4
441
2/125 2/125 2
12
5
551
3/18 3/132 31
32
221
16
25
3 8
New notation for a familiar concept!
Denominator is the index (root) of the radical.
3/127 3273
Evaluate:Evaluate:
2/125 525
5/132 2325
3/1343 73433
4/181 3814
Evaluate:Evaluate:
4/181
3/11000 1010003
3/18 283
Not a real number
3/18
21
81
81
33/1
4 81
2/122a a22
Rewrite in Radical Notation:Rewrite in Radical Notation:
8/1w
2/13x 3 x
8 w
2/34 32/14
Rational ExponentsRational Exponents
32 8
Numerator is the power.
2/34 2/134 2/164 8
ba
xpower
root
Generally easier to find the root first and then the power.
3/227 92723
Evaluate:Evaluate:
2/325
4/581 2438154
3/227
91
27
127
1233/2
125253
3/21000 100100023
Evaluate:Evaluate:
4/316
5/332 83235
5/31 1
81634
Slide 10- 11Copyright © 2011 Pearson Education, Inc.
Simplify.
a) 4
b)
c) 4
d)
2/38
1
4
1
4
Slide 10- 12Copyright © 2011 Pearson Education, Inc.
Simplify.
a) 4
b)
c) 4
d)
2/38
1
4
1
4
8 33 8/133
Write in Exponential Form:Write in Exponential Form:
7 5r
7 3
5
n 7/3
5n
83 m 3/8m
7/5r
Rules of ExponentsRules of Exponents
32 xx 532 xx
2/13/2 nn 63
64
n2
1
3
2
n 6
1
n
Rules of ExponentsRules of Exponents
52 32 xx 76x
2/35/4 48 cc 1015
108
32
c2
3
5
4
32
c 10
23
32c
Rules of ExponentsRules of Exponents
2
5
xx
325 xx
2/1
8/5
xx 8
485
x21
85
x 81
x
Rules of ExponentsRules of Exponents
32x 632 xx
5/22/3m 53
m5
2
2
3
m
Simplify radical expressions:Simplify radical expressions:
4 36
4/136 4/126 41
12
6
21
6 62
1
Simplify radical expressions:Simplify radical expressions:
6 27
6/127 6/133 61
13
3
21
3 32
1
Simplify radical expressions:Simplify radical expressions:
10 82ba
10/182ba 10
18
10
12
ba 54
51
ba 51
4ab 5 4ab
Simplify radical expressions:Simplify radical expressions:
3 25 4 xx
3
2
5
4
xx 1510
1512
x 15
22
x 15 22x
Simplify radical expressions:Simplify radical expressions:
4 5 z
45
1
z4
1
5
1
z 20
1
z 20 z
Slide 10- 23Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
3/ 41/ 2 2 /3x y
3/8 1/ 4x y
3/8 3/ 4x y
3/8 1/ 2x y
3/ 4 1/ 2x y
Slide 10- 24Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
3/ 41/ 2 2 /3x y
3/8 1/ 4x y
3/8 3/ 4x y
3/8 1/ 2x y
3/ 4 1/ 2x y