7.1/7.2i Notes 2011
n-th Roots and Rational Exponents
Properties of Rational Exponents & Important Numbers
Exponent Rules Review
a
m
a
am
an
n
(ab) m
a
m
a
b
(a m ) n
Jedi create light, but the Sith do not create darkness.
They merely use the darkness that is always there.
am
bm
am bm
1
m
a
a0
m
Examples:
In this lesson we will extend the concept of square roots to other types of roots. Our goal will be to evaluate nth roots of real numbers
using both radical notation and rational (fractional) exponent notation.
a.
c.
25
3
27
1
2
25 =
b.
3
8
d.
5
32
8
1
3
x
1
x
2
x
3
x
4
x
5
x
6
x
7
x
8
x
9
x
10
x
1
1
2
3
4
5
6
7
8
9
10
2
1
4
9
16
25
36
49
64
81
100
3
1
8
27
64
125
216
343
512
729
1000
4
1
16
81
256
625
1296
2401
4096
6561
10000
5
1
32
243
1024
3125
7776
16807
32768
59049
100000
6
1
64
729
4096
15625
46656
117649
262144
531441
1000000
7
1
128
2187
16384
78125
279936
823543
2097152
4782969
10000000
8
1
256
6561
65536
390625
1679616
5764801
16777216
43046721
100000000
9
1
512
19683
262144
1953125
10077696
40353607
134217728
387420489
1000000000
10
1
1024
59049
1048576
9765625
60466176
282475249
1073741824
3486784401
10000000000
Find the indicated real nth root(s):
Example 1:
a)
5
d)
729 6
b)
1024
4
81
1
e)
7776
Example 2
Translate to radical form:
4
a)
53
4
10
b)
c)
7
9
13 3
d)
( 2)
c)
36 2
2
5
Example 3
Simplify the following
3
c)
d)
e)
3
125
2
4
3
4
7
( 16 )
( 81 )
7
f)
( 2097152 ) 7
128
1
1
4
More complicated rational exponents:
Translate to fractional form:
c)
d)
e)
25
5
2
( 64 )
5
3
Using properties of rational exponents
Example 4
a.
5
1
4
5
3
4
b.
1
3
(3 )
2
5
c.
1
2
80
1
16 2
3
d.
2
1
4
8
1
4
e.
12 5
12
g.
3
(x )
1
2
h.
(4
3
f.
1
5
3
2 )
13
i.
x
1
2
x
181 4
91 4
1
5
3