P2
Exponents & Radicals
What does an exponent tell you??
Repeated Multiplication
How many times you multiply the base by
itself.
Expand the following:
x 
5
( 3) 
5
2y 
5
General Rule on Negatives:
 
 
even

odd

Properties of Exponents
Examples
a) (4m n )(5mn )
2
2
3
b) (2 x y )
4
c) 6 x(3x )
4
 6x
d) 
 y
4



1
3
2
0
e)  (2 x y )
2
4
f)
2
6x
2
 4a
g)  3
 y
2



3
3
Try Some Harder Ones
4
2
25 x y
1
15 x y
 2x y 


4
 4y 
3
4( x  y )
24( x  y )
3
2
3
Scientific Notation
1.
2.
3.
4.
2.468  10
0.00000815
5
7
6.54  10
9,876,000,000
Radicals and their Properties
Square Root
Cube Root
One of its two equal
factors
One of its three equal
factors
If a and b are real numbers, n  2 , then
a
n
1
n
b
b is the nth root of
a b 
b is the nth root of
n index
a  radicand
a
a
Examples
1. 49
2.  49
4.  32
5.
5
4
 16
3.
3
8
125
Properties of Radicals
 a
m
1.
n
a 
2.
n
a  n b  n ab
m
n
n
a na
3. n 
b0
b
b
4.
5.
m n
a  mn a
 a
n
n
a
6. For n even, n a n  a
For n odd,
n
an  a
Let’s Look at Property #6
6. For n even, n a n  a
For n odd, n a n  a
Ok… think about this
49  ?
What are the solutions to this?
x  49
2
Let’s Try a few
3
x y
6
4
5
x y
2
6
7
x y
7
3
4
3
x y
Simplifying Radicals
No denominators with Radicals &
All numbers and exponents in simplest form
List:
All perfect squares from 1- 15
All perfect cubes from 1- 6
All perfect fourths from 1- 4
All perfect fifths from 1- 4
Warm-up
1.
4
48
75 x 3
2.
3.
4
4.
3
5.
3
6.
3
7.
3
8 x 
4
24
54a
4
 40 x
16 x
6
4
7
8
8.
48 x y
9.
50 x 2 y 4
Adding and Subtracting Radicals
must be “like radicals”
(same index and radicand)
Examples
1.
2.
2 48  3 27
3
16 x  54 x
3
4
Rationalizing
Denominators & Numerators
7
Ex. 1
Ex. 2
3 2
3
3
6
Ex. 3 (with 2 terms in the denominator)
3
4 2
Ex. 4 (with 2 terms in the numerator)
3 5
2
Now You Try Some
4

3
6

3 9
4

3 2
8

2
3
3x
Rational Exponents
1.
a
2.
a
1
n
m
n
n a
m
  a n  


1
 a
m
n
Examples
x x
2
3
8 
2
27
3
3
5
6 6
1
5
32 5 
3
3
2
2

 1 


 100 
3
2

 a
n
m