Download 7-6A Rational Exponents

Algebra 2
7.6 Rational Exponents
Obj: able to use properties of rational exponents to simplify expressions.
Rational Exponents
If a is a non-zero real number and m and n are integers, then
1
m
an = n a
Ex:
1
16 4
a n = n am =
and
= 4 16 = 2
Ex.
2
32 5
( a)
m
n
= 32 2 =
5
.
If m is negative, then
( 32 )
5
2
= 22 = 4
Rewrite in radical form, and then simplify.
1.
1
125 3
a≠0
Rewrite in rational exponent form.
2. 2430.4
3.
3
27
4.
3
2 f 2g6
Simplify. Putting answer in same format as original problem.
1
5.
4
49x
2
6.
y2 +2
1
y2 −2
Properties of Rational Exponents
Let a and b be real numbers, and let m and n be integers.
1. a ⋅ a = a
m
n
Ex. 2
5. a
Ex.
−n
4
2
3
=
−
⋅2
m+ n
2.
(a )
m n
=a
 12 
Ex.  2 
 
 
1
3
1
,a ≠ 0
an
6.
m• n
3.
6
(ab )
m
=a b
m
am
4.
= a m−n , a ≠ 0
n
a
m
( )
Ex. 3x
1
2 2
Ex.
2
3
2
1
22
1
= an,a ≠ 0
−n
a
m
am
a
=
,b ≠ 0

bm
b
7. 
1
1
2
Ex.
1
9
I don’t get
it at all
1
What do you still need to work on?
I sort of
get it
2
−
1
2
 3 3
Ex.  
8
Rate yourself on how well you understood this lesson.
I understand
I understand
most of it but I
it pretty well
need more practice
3
4
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5