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7.2 Properties of Rational Exponents
2/21/2014
Review of Fractions
• Adding Fractions with same denominators:
= 2
Review of Fractions
• Adding Fractions with unlike denominators:
Multiples of 4: Multiples of 3:
Find Least Common Multiple:
Review of Fractions• Multiplying fractions: you don’t need common
denominators!• Multiply the numerators and denominators,
then reduce if necessary.
Example 1 Use Properties of Rational Exponents
a. 62/3 • 61/3 = 6(2/3 + 1/3) = 63/3 = 61 = 6
b. (33/4)4 = 3(3/4 4)• = 33 = 27
c. (16 • 25)1/2 = 20= 161/2 • 251/2 = 4 • 5
d. 8 1/3–1
=81/3 =
2
1
e.71/2
75/2
= 7(5/2 1/2)– = 74/2 = 72 = 49
¿1
3√8
¿√16 ∙√25
Fourth RootPerfect Fourth
1 = 14
16 = 24
81 = 34
256 = 44
625 = 54
4√1=14√16=24√81=34√256=4
4√625=5
Fifth RootPerfect Fifth1 = 15
32 = 25
243 = 35
1024 = 45
3125 = 55
5√1=15√32=25√243=35√1024=45√3125=5
Simplifying
2552 33 3 82
44 4 6255 55 5 2433
=5=2=5=3
In general aan n
Properties of Radicals
Product property:
Quotient property:
Example 2 Use Properties of Radicals
a. 33 • 93
= 3 Simplify.
= 4
3
48 Quotient property of radicals
= 2 Simplify.
= 33 • 9 Product property of radicals
= 33 • 3 Factor.• 3
b.4 48
34
4 16
3 33
𝑜𝑟 3√3 ∙ 9= 3√27=𝟑
Example 3 Write Radicals in Simplest Form
a. 3 40 = 83 • 5 Factor out a perfect cube.
= Separate the product83 • 53
= 2 Simplify.53
5√64b. = Factor out a perfect fifth.
=
Checkpoint
Simplify the expression.
Use Properties of Radicals and Rational Exponents
ANSWER 2
ANSWER 2
ANSWER 3
ANSWER 3
1. 23 • 43
2. 45 • 85
3. 543
23
4. 813
33
Example 5 Simplify Expressions with Variables
a. 9x 6
Simplify the expression. Write your answer using positive exponents only. Assume all variables are positive.
= 3x 3
b. 4y 6 ( )1/2 = 41/2 y 6 ( )1/2
= y (6 · 1/2)
= 2y 3
= = =
Example 5 Simplify Expressions with Variables
c. 3
y 6
x 3
=x
y 2
d.ac 2
3a 3/2 c
–
3a (3/2 1)c 3= –
3a 1/2c 3=
¿ ( 𝑥3
𝑦6 )13 ¿ 𝑥
( 3 ∙1 /3 )
𝑦(6 ∙
13
)
¿𝟑𝒄𝟑√𝒂or
=
𝑒 .√𝑥 𝑦2𝑧 3
Example 5
¿ (𝑥 𝑦2 𝑧3 )12
In radical form: any fractional exponent more than 1 (improper fraction), change fractional exponent to mixed number.
¿ 𝒚 ∙ 𝒛 ∙ 𝒙𝟏𝟐 ∙ 𝒛
𝟏𝟐
¿ 𝑦𝑧 √𝑥 ∙√𝑧¿ 𝒚𝒛 √𝒙𝒛
Checkpoint
Simplify the expression. Write your answer using positive exponents only. Assume all variables are positive.
ANSWER 5y 2
ANSWER 2uv 3
1. 25y 4
ANSWER 2x 2/3z 3
Simplify Expressions with Variables
2. y 2
x 6ANSWER
yx 3
3. 8u 3v 9( )1/3
4. 2xx 1/3z 3–
Homework: 7.2 p.362 #21-43 odd,
51-65 oddskip #35
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