1

Algebra 2: Section 7.2

Properties of Rational Exponents(Day 1)

2

Using Properties of Rational Exponents

Same properties as last chapter See p.407 or notes from Section 6.1 for a

summary of properties

3

Simplifying Rational Exponents

Use all properties of exponents All exponents must be positive Only one base occurs in each term (unless

denominator has to be rationalized) Exponent of denominator must be a whole

number (rationalized)

4

Examples: Simplify

11

321. 6 61 1

2 36

3 2

6 66

5

66

5

Examples: Simplify

21 1

3 42. 27 6

2 2

3 427 61

3 2 227 6 1

2 23 6 1

29 6

6

Examples: Simplify

1

3 3 33. 4 2

1

3 3 3

1

4 2 1 1

1

4 2

1

8

13 3(4 2)

Alternate Method

13 3(8)

181

8

7

Examples: Simplify

3

4

64.

63

146

1

46

8

Examples: Simplify

31

4

1

4

185.

9

31 1

4 4

1

4

9 2

9

31

42

3

42Alternate Method

31418

9

31

42

3

42

9

Properties of Radicals

n

n

Product Property: a

aQuotient Property:

n n

nn

b a b

a

bb

10

Simplifying Radical Expressions

All numbers under radical must be simplified No exponent under the radical larger than

the root May be easier to change to rational

exponents, simplify, then change back

11

Examples: Simplify

3 36. 25 5

3 125 5

3 32 15 5 5Alternate Method

3 35

12

Examples: Simplify

3

3

327.

4

332

43 8 2

13

Examples: Simplify

48. 6444 16 4 42 4

Alternate Method

4 62 4 44 22 2 42 4

14

Homework

P.411#22-41 all