3.2 Apply Properties of Rational Exponents

Do properties of exponents work for roots?What form must they be in?

How do you know when a radical is in simplest form?

Before you can add or subtract radicals what must be true?

Properties of Rational Exponents

aaanmnm

aamnnm

baab mmm

0,1

a

aa m

m

0, aa

aa nm

n

m

0,

bba

ba

m

mm

554121

23121

58

4144

32

731

7

2

31

31

412

= (71/3)2

= 12 –1

Use the properties of rational exponents to simplify the expression.

b. (61/2 41/3)2 = (61/2)2 (41/3)2 = 61 42/3 = 6 42/3= 6(1/2 2) 4(1/3 2)

e.421/3 2

61/3= 7(1/3 2) = 72/3

a. 71/4 71/2= 7(1/4 + 1/2) = 73/4

= 12[5 (–1/5)]c. (45 35)–1/5 = [(4 3)5]–1/5 = (125)–1/5 1

12=

d.

5

51/3= 5(1 – 1/3) = 52/3

51

51/3=

=42

6

1/3 2

This is a good example I why I have been complaining about the book slides. This is how it copies…

Now see what changes I made…

= (71/3)2

= 12 –1

Use the properties of rational exponents to simplify the expression.

b. (61/2 • 41/3)2 = (61/2)2 • (41/3)2 = 61 • 42/3 = 6 • 42/3= 6(1/2 • 2) • 4(1/3 • 2)

e.421/3 2

61/3= 7(1/3 • 2) = 72/3

= 7(1/4 + 1/2) = 73/4

= 12[5 • (–1/5)]c. (45 • 35)–1/5 = [(4 • 3)5]–1/5 = (125)–1/5 1

12=

d.

5

51/3

= 5(1 – 1/3) = 52/351

51/3=

=42

6

1/32

Write the expression in simplest form

3 54

5

4

3

You need to rationalize the denominator—no tents in the basement

Adding and subtracting like radicals and root.

When adding or subtracting like radicals the root and the number under the radical sign must be the same before you can add or subtract coefficients.

Radical expressions with the same index and radicand are like radicals.

You may need to simplify the radical before you can add or subtract.

Adding & Subtracting Roots and Radicals

665151

27

33 216

Simplify the expression involving variables

63 125y

21102

9 vu

4 8

4

yx

zy

x

x531

21

2

6

Write the expression in simplest form

5 13955 cba

3 7

yx

Add or subtract the expression involving variables.

yy 65

3131 72 xyxy

3 23 5 4053 xxx

• Do properties of exponents work for roots?Same rules apply.• What form must radical be in?Fractional exponent form• How do you know when a radical is in

simplest form?When there are no more numbers to the root

power as factors of the number under the radical.

• Before you can add or subtract radicals what must be true?

The number under the radicals must be the same.

3-2 Assignment

p. 176, 3-63 every 3rd

Write down the problem