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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
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)!!
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
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