View
227
Download
0
Category
Preview:
DESCRIPTION
Simplify:
Citation preview
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
Recommended