objective: 7.2 properties of rational exponents1 homework answers 14. 11 1/3 38. -1/125 16. 16 5/9...
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Objective: 7.2 Properties of Rational Exponents 1
Homework Answers
14. 11 1/3 38. -1/125
16. 16 5/9 40. 1/25
18. 42. 2.18
20. 44. 1.15
22. 48. -11.19
30. -10 54. -6
32. ½ 56. 0
34. -4 58. -1.41, 1.41
36. 1/81 60. 3.30 66. 2.13
3 637 )10(
74 )8(
Objective: 7.2 Properties of Rational Exponents 2
So Much to Learn!
By the end of today, you should be able to:1. Simplify expressions with rational
exponents.2. Use properties of rational exponents.3. Write an expression involving rational
exponents in simplest form.4. Perform operations with rational exponents.5. Simplify expressions that have variables
and rational exponents.6. Write an expression involving variables and
rational exponents in simplest form.7. Perform operations with rational exponents
and variables.
Objective: 7.2 Properties of Rational Exponents 3
Properties of Rational Exponents
Properties of Rational Exponents:
Property: Example:
1.
2. (am)n = amn
3. (ab)m = ambm
4.
nmnm aaa
Notes
93333 2)2
3
2
1(
2
3
2
1
6444)4( 3)22
3(22
3
62349)49( 2
1
2
1
2
1
0,1
aa
am
m
5
1
25
125
2
12
1
Objective: 7.2 Properties of Rational Exponents 4
Properties of Rational Exponents (cont.)
Properties of Rational Exponents:
Property: Example:
5.
6.
0, aaa
a nmn
m
Notes
3666
6
6 2)2
1
2
5(
2
1
2
5
0,)( ab
a
b
am
mm
3
2
27
8)
27
8(
3
1
3
1
3
1
Objective: 7.2 Properties of Rational Exponents 5
Using the Properties
Simplify the expressions:1.
2.
3.
4
1
2
1
55
23
1
2
1
)58(
4
144 )32(
Objective: 7.2 Properties of Rational Exponents 6
More Fun with Properties
4.
5.
3
1
7
7
2
3
1
3
1
)
4
12(
Objective: 7.2 Properties of Rational Exponents 7
You Try
Simplify:1.
2.3.4.
5.
3
4
1
4
1
3
2
3
133
24
1
3
1
3
1
2
1
9
18
6
6
)24(
)627(
66
Objective: 7.2 Properties of Rational Exponents 8
More Simplifying
Simplify the expressions:1.
2.
33 164
4
4
2
162
Objective: 7.2 Properties of Rational Exponents 9
You Try
Simplify:1.
2.
33 525
3
3
4
32
Objective: 7.2 Properties of Rational Exponents 10
Simplest Form - continued
In order for a radical to be in simplest form, you have to remove any perfect nth powers and rationalize denominators. Example:
Write in simplest form:1. 2. 3 54 5
4
3
Objective: 7.2 Properties of Rational Exponents 11
You Try
Write in simplest form:
4
4
8
7
64
Objective: 7.2 Properties of Rational Exponents 12
Operations Using Radicals
Two radicals expressions are “like radicals” if they have the same index and the same radicand. Example:Perform the indicated operation:
1. 2. )6(2)6(7 5
1
5
1
33 216
Objective: 7.2 Properties of Rational Exponents 13
You Try
Perform the indicated operation:
33
4
3
4
3
381
)4(3)4(5
Objective: 7.2 Properties of Rational Exponents 14
Simplifying Expressions Involving Variables
Important!
= x when n is odd.
= |x| when n is even.
nn x
nn x
Objective: 7.2 Properties of Rational Exponents 15
Simplifying
Simplify the expression. Assume all variables are positive:
1. 2.
3. 4.
3 6125y 2
1102 )9( vu
48
4
y
x
53
1
2
1
2
6
zx
xy
Objective: 7.2 Properties of Rational Exponents 16
You Try
Simplify the expression. Assume all variables are positive.
1.
2.3.
4.
34
1
3
2
410
5
2
124
3 9
6
18
)16(
27
tr
rs
y
x
hg
z
Objective: 7.2 Properties of Rational Exponents 17
Writing Variable Expressions in Simplest Form
Write the expression in simplest form. Assume all variables are positive.
1. 2. 5 13955 cba 37y
x
Objective: 7.2 Properties of Rational Exponents 18
You Try
Write the expression in simplest form. Assume all variables are positive.
57
2
4 149412
h
g
fed
Objective: 7.2 Properties of Rational Exponents 19
Adding and Subtracting Expressions Involving Variables
Perform the indicated operation. Assume all variables are positive.
1. 2.
3.
yy 65 3
1
3
1
72 xyxy
3 23 5 4053 xxx
Objective: 7.2 Properties of Rational Exponents 20
You Try
Perform the indicated operations. Assume all variables are positive.
1.
2.
3.44 5
4
1
4
1
662
63
38
xxx
ghgh
xx
Objective: 7.2 Properties of Rational Exponents 21
Homework
Homework:page 411, 22-30 even, 34-62 even, 66-72 even, 76, 80