7.2 Properties of Rational ExponentsOBJ: use properties of rational exponents & radicals and write expressions in simplest form

Do Now: Simplify

a)(-5)4 · (-5)5 b) (2xy3)4 c) (8)-2

d) e) (7b-3)2 b5 b 3

5

x

x

Product Property a amm ·· a ann=a=am+nm+n

Power of a Power Property (a (amm))nn=a=amnmn

Power of a Product Property (ab)(ab)mm=a=ammbbmm

Negative Exponent Property a a-m-m= = aa≠0≠0

Zero Exponent Property a a00=1 =1 a≠0a≠0

Quotient of Powers aamm = a= am-n m-n a≠0a≠0 a ann

Power of Quotient b≠0b≠0

Review Of Properties of Exponents

ma

1

Do Not Copy

m

mm

b

a

b

a

c) (4 (433 · 2 · 233))-1/3-1/3

(4(433))-1/3-1/3 · (2 · (233))-1/3-1/3

44-1-1 · 2 · 2-1-1

¼¼ · · ½½

11//88

d)

***The SAME properties that apply to integer exponents apply to rational

exponents (no decimal answers)

a) 6 61/21/2 · 6 · 61/31/3 661/2 + 1/31/2 + 1/3 * on calculator: (1/2)+(1/3)

enter MATH Frac

665/65/6

b) (27(271/31/3 · 6 · 61/41/4))22

(27(271/31/3)) 2 2 · (6 · (61/41/4))22

27272/32/3 · 6 · 62/42/4

((33√27)√27)22 · 6 · 61/21/2 3322 · 6 · 61/21/2

99 · 6· 61/21/2

Ex 1:

3/17

7

)3/11(7

3/27

Review of Properties of Radicals

Product PropertyProduct Property

Quotient PropertyQuotient Property

baab

10210410440

b

a

b

a

2

3

4

3

4

3

Do Not Copy

Write the expression in simplest

form.

a) = = = =

==

b) = b) =

= = = =

==

*** If the problem is in radical form to begin with, the answer should be in radical form as well

a)a) b) b)

55

22

33 525

3 )5)(25(

3 125

3

3

4

32

3

4

32

3 8

Ex 2:

Ex 3:

4 64 4 416 44 416

4 4 2

4

8

74

4

8

7

4

4

4

4

2

2

8

7

4

4

16

14

2

144

No tents in the basement!

Ex4: Perform the indicated operation

a) 5(45(43/43/4) – 3(4) – 3(43/43/4))

2(42(43/43/4))

b) b)

c) c)

33 381

33 3327 33 333

3 32

33 5625 33 55125

33 555 3 5 6

If the original problem is in radical form,

the answer should be in radical form as well.

If the problem is in rational exponent form, the answer should be in rational exponent form.

*** Combine “like terms”

HW

Day 2: PracticeDay 2: Practice

continued…

OBJ: use properties of rational exponents & radicals and write variable expressions in simplest form

Do Now: Simplify1)1)

2)2)

3)3)

4) 4)

2x x

6 6x x

11 11y y

4 8r 4 44rr

rr 2r

Ex 1: Simplify the Expression

a)a)

b) (16gb) (16g44hh22))1/2 1/2

= 4g= 4g22hh

c) c)

3 927z 33z

510

5

y

x

2y

x

d)34

1

3

2

6

18

tr

rs

33

2

4

3

3 tsr

4 232 12effde

Ex 2: Write the expression in simplest form.

a) a) 4 149412 fed

b) 57

2

h

g

No tents in the basement!

2

5 32

h

hg

c)4

3

23

5

15df

fed 53

223 fed

** Remember, solutions must be in the same form as the original problem (radical form or rational exponent form)!!

d) d) 46

118

z

yx

No tents in the basement

2

4 2322

z

zyyx

Ex 3: Perform the indicated operation.

a) xx 38 x5

b) 4

1

4

1

63 ghgh 4

1

3gh

c) 44 5 662 xxx 44 662 xxxx 4 63 xx

d) sss 26 s126 s5

e) 323 7 6263 yyy

3232 6263 yyyy

32 65 yyHW: