1. Apply Properties of Rational Exponents
Section 6-2 Day 1
Apply Properties of Rational Exponents

2. Properties of Radicals
Product Property of Radicals
𝑛 𝑎∙𝑏 = 𝑛 𝑎 ∙ 𝑛 𝑏
Quotient Property of Radicals
𝑛 𝑎 𝑏 = 𝑛 𝑎 𝑛 𝑏
4 16𝑥
= ∙ 4 𝑥
=2 4 𝑥

3. 13 = = = 1
23 = = = 32
33 = = = 243
43 = = = 1024
53 = = = 3125
63 = 216
73 = 343
83 = 512

4. Example 1
Use the properties of rational exponents to simplify the expression.
a.) ∙ =
b.) ( ∙ ) 3 =
c.) ( 2 6 ∙ 4 6 ) −1 6 =
d.) =
( ) 3 ∙ ( ) 3 = 5∙
( 2 6 ) −1 6 ∙ ( 4 6 ) −1 6 =
2-1 • 4-1 =
½ • ¼
= ⅛ 1
10 1− = =

5. Example 2 Use the properties of radicals to simplify the expression.
b.) =
5 • 2 = 10
5 32 ∙ = 2

6. Example 3 Write the expression in simplest form. a.) 3√104 =
3√8 • 3√13 =
2 3√13

7. Example 4 Simplify the expression. a.) 7 5√12 – 5√12 =
b.) 4( ) + 8( ) = 1
6 5√12
12( )

8. Warm-Up Use the properties of radicals to simplify the expression.
4 8 ∙ 4 8
Write the expression in simplest form.
3 104
3 135

9. Apply Properties of Rational Exponents
Section 6-2 Day 2
Apply Properties of Rational Exponents

10. Example 5 Simplify the expression. a.) 4√625z12 = b.) (32m5n30)1/5 =
c.) 3√6x4y9z14 =
5z3
5√32m5n30 =
2mn6
3 √6 • 3√x3 • 3√x • 3√y9 • 3√z12 • 3√z2 =
xy3z4 3√6xz2

11. Example 6 Simplify the expression. a.) 4√12 – 2√75 =
b.) 6 3√ √24 =
4•√4 •√3 – 2√25 •√3
4• 2•√3 – 2 • 5 •√3
8√3 – 10√3
= -2√3
6 3√27 • 3√ √8 • 3√3
6 • 3 3√ • 2 3√3
18 3√ √3
= 32 3√3

12. Homework Section 6-2 Pages 424 –425
3, 4, 6, 8, 11, 15, 17, 18, 20, 21, 23, 24, 26 – 28, 33, 35,
36, 40, 43 – 48, 52, 53, 57, 60, 62, 64, 69, 78, 79