Download 3.2 Apply Properties of Rational Exponents

3.2 Apply Properties of Rational
Exponents
Do properties of exponents work for roots?
What form must they be in?
How do you know when a radical is in simplest
form?
Before you can add or subtract radicals what
must be true?
Properties of Rational Exponents
a a  a
m
n
 
n
m 
a
a
mn
ab  a b
m
a
m

m
m
1
a
m
a a
a
a a
 
b b
m

13 2

2  3 
4 1 4
4
,a  0
mn
n
m
5 5
8  5 
12
mn
14
12
7
,a  0
7

12
 13
 4
13
m
m
1 3
,b  0




2

This is a good example I why I have been complaining
about the book slides. This is how it copies…
Use the properties of rational exponents to simplify the expression.
a.
71/4 71/2 = 7(1/4 + 1/2)= 73/4
b.
(61/2 41/3)2 = (61/2)2 (41/3)2 = 6(1/2 2) 4(1/3 2) = 61 42/3 = 6 42/3
c.
(45 35)–1/5 = [(4 3)5]–1/5 = (125)–1/5 = 12[5 (–1/5)] = 12 –1 =
1
12
d.
e.
51
= 5(1 – 1/3)= 52/3
=
51/3 51/3
421/3 2
42 1/3 2
=
= (71/3)2 = 7(1/3 2) = 72/3
61/3
6
5
Now see what changes I made…
Use the properties of rational exponents
to simplify the expression.
= 7(1/4 + 1/2) = 73/4
b.
(61/2 • 41/3)2
c.
(45 • 35)–1/5
= (61/2)2 • (41/3)2
= [(4 • 3)5]–1/5
= 6(1/2 • 2) • 4(1/3 • 2)
= (125)–1/5
= 12[5 • (–1/5)]
= 61 • 42/3 = 6 • 42/3
= 12 –1 =
1
12
d.
5
=
51/3
e.
421/3
61/3
51
= 5(1 – 1/3)
= 52/3
51/3
2
=
42
6
1/3
2
= (71/3)2
= 7(1/3 • 2)
= 72/3
Write the expression in simplest
form
3
54
5
3

4
You need to rationalize the denominator—
no tents in the basement
Adding and subtracting like
radicals and root.
 When adding or subtracting like radicals the root
and the number under the radical sign must be
the same before you can add or subtract
coefficients.
 Radical expressions with the same index and
radicand are like radicals.
 You may need to simplify the radical before you
can add or subtract.
Adding & Subtracting Roots and
Radicals
  26  
15
15
76
3
16  2 
3
Simplify the expression involving
variables
3
125 y 
6
9 u v 
10 1 2
2

4
4
x
y

8
12
6x y
13
2x
z
5

Write the expression in simplest form
5
5 9 13
5a b c
x
3
y
7

Add or subtract the expression
involving variables.
5 y 6 y 
2 xy  7 xy 
13
13
3 5x  x 40x 
3
5
3
2
• Do properties of exponents work for roots?
Same rules apply.
• What form must radical be in?
Fractional exponent form
• How do you know when a radical is in
simplest form?
When there are no more numbers to the root
power as factors of the number under the
radical.
• Before you can add or subtract radicals
what must be true?
The number under the radicals must be the
same.
3-2 Assignment
Write down
the problem
p. 176, 3-63 every 3rd