Properties of Rational Exponents Section 7.2. WHAT YOU WILL LEARN: 1. Simplify expressions with...
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Transcript of Properties of Rational Exponents Section 7.2. WHAT YOU WILL LEARN: 1. Simplify expressions with...
Properties of Rational Exponents
Section 7.2
WHAT YOU WILL LEARN: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.
Properties of Rational Exponents
nmnm aaa
Properties of Rational Exponents:
Property: Example:
1.
2. (am)n = amn
3. (ab)m = ambm
4.
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
Properties of Rational Exponents (cont.)
0, aaa
a nmn
m
Properties of Rational Exponents:
Property: Example:
5.
6.
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
Using the Properties
4
1
2
1
55
• Simplify the expressions:
1.
2.
3.
23
1
2
1
)58(
4
144 )32(
More Fun with Properties
3
1
7
74.
5. 2
3
1
3
1
)
4
12(
You Try
3
4
1
4
1
3
2
3
133
24
1
3
1
3
1
2
1
9
18
6
6
)24(
)627(
66
• Simplify:
1.
2.
3.
4.
5.
More Simplifying
33 164
• Simplify the expressions:
1.
2.
4
4
2
162
You Try
33 525
• Simplify:
1.
2. 3
3
4
32
Simplest Form - continued
3 54
• 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. 5
4
3
You Try
4
4
8
7
64
• Write in simplest form:
1.
2.
Operations Using Radicals
)6(2)6(7 5
1
5
1
• Two radicals expressions are “like radicals” if they have the same index and the same radicand. Example:
• Perform the indicated operation:
1. 2. 33 216
You Try
33
4
3
4
3
381
)4(3)4(5
• Perform the indicated operation:
1.
2.
Simplifying Expressions Involving Variables
nn x
• Important!
= x when n is odd.
= |x| when n is even.
nn x
Simplifying
3 6125y
• Simplify the expression. Assume all variables are positive:
1. 2.
3. 4.
2
1102 )9( vu
48
4
y
x53
1
2
1
2
6
zx
xy
You Try
34
1
3
2
410
5
2
124
3 9
6
18
)16(
27
tr
rs
y
x
hg
z
• Simplify the expression. Assume all variables are positive.
1.
2.
3.
4.
Writing Variable Expressions in Simplest Form
5 13955 cba
• Write the expression in simplest form. Assume all variables are positive.
1. 2. 37y
x
You Try
57
2
4 149412
h
g
fed
• Write the expression in simplest form. Assume all variables are positive.
1.
2.
Adding and Subtracting Expressions Involving Variables
yy 65
• Perform the indicated operation. Assume all variables are positive.
1. 2.
3.
3
1
3
1
72 xyxy
3 23 5 4053 xxx
You Try
44 5
4
1
4
1
662
63
38
xxx
ghgh
xx
• Perform the indicated operations. Assume all variables are positive.
1.
2.
3.
Homework
page 411, 22-30 even, 34-62 even, 66-72 even, 76, 80
: