1. Apply Properties of Rational Exponents
Section 6.2
Apply Properties of Rational Exponents

2. Opener 6.2 1. Simplify : 2. Simplify: 3. True or False: 4. Simplify:
6. Evaluate:
7. Evaluate:
True
False

3. Copy these on your Power Card

4. = 73/4 = (61/2)2 (41/3)2 = 6(1/2 2) 4(1/3 2) EXAMPLE 1
Use properties of exponents
Use the properties of rational exponents to simplify the expression.
a /4 71/2
= 7(1/4 + 1/2)
= 73/4
b. (61/2 41/3)2
= (61/2)2 (41/3)2
= 6(1/2 2) 4(1/3 2)
= /3
= 6 42/3 1 12 =
c. (45 35)–1/5
= [(4 3)5]–1/5
= (125)–1/5
= 12[5 (–1/5)]
= 12 –1 d. 5
51/3 51
51/3 =
= 5(1 – 1/3)
= 52/3 = 42 6
1/3 2 e.
421/
61/3
= (71/3)2
= 7(1/3 2)
= 72/3

5. Review of computing with fractions

6. Examples:
Can’t combine they are not the same base: aman=am+n

7. EXAMPLE 3
Use properties of radicals
Use the properties of radicals to simplify the expression. a. 12 3 18 3 =
216 3 = = 6
Product property b. 80 4 5 80 5 4 = = 16 4 = 2
Quotient property

8. Radical Examples!