7.2: Properties of Rational

ExponentsObjectives: Students will be able to…• Use properties of rational exponents

to evaluate and simplify expressions

Examples:

THE PROPERTIES OF EXPONENTS WE LEARNED IN SECTION 6.1 ARE THE SAME FOR RATIONAL EXPONENTS!!!

2384

21

32

3

2

23

35

34

31

6444

yxyx

xxx

32

27

8278

1

1

31

31

31

222

425

21

25

21

41

41

yyyy

y

y

xx

Simplify:

3

41

41

43

31

33

2

41

31

31

21

9

18.)

6

6.)

24.)

627.)

66.)

e

d

c

b

a

1.

2.

Using Properties of Radicals to Simplify

33 525

3

3

432

1.

2.

For a radical to be in simplest form, you must remove any perfect nth powers (other than 1) and rationalize any denominators

4 64

4

87

Multiply top and bottom by a quantity that will make the denominator a perfect 4th power.

1.

2.

Write in simplest form.

3 000,10

4

32

Can only add or subtract radical expressions if

they are like radicals (just like combining like terms!!)

Examples:1.)

2.)

Like Radicals: same index, same radicand

)3(4)3(6 32

32

33 381

1.

2.

You try…Perform indicated operation

4

343

43)4(5

33 5625

Rewrite radicand so exponents match index, if

possible Take out any expressions that match the index Can apply any rule of exponents

Simplifying Radicals with Variables(assume all variables positive)

Examples: Simplify

341

32

510

5

21

24

3 9

6

18.)4

.)3

16.)2

27.)1

tr

rs

yx

hg

z

Write the expression in simplest

form.

57

2

4 1494

.)2

12.)1

hg

fed

Make denominator perfect 5th root…multiply by h3 on top and bottom

You try!! Simplify

4

32

2

41

48

3 1053

515.)3

625.)2

8.)1

dffed

kj

tsr

Challenge…Simplify

46

118

zyx

Perform indicated operation. Assume all

variables positive.

To add or subtract radical expressions involving variables, you also need like radicals (may need to simplify first!!)

323 7

31

231

2

6263.)3

64.)2

26.)1

yyy

nmnm

sss

NOT LIKE RADICALS!!

You try…perform indicated

operation.

44 5

41

41

662.)3

63.)2

38.)1

xxx

ghgh

xx