p2 exponents & radicals. what does an exponent tell you?? repeated multiplication how many times...

P2Exponents & Radicals

What does an exponent tell you??

Repeated Multiplication

How many times you multiply the base by itself.

Expand the following:

5

5

5

2

)3(

y

x

odd

even

General Rule on Negatives:

Properties of Exponents

Examples

24

3

3

2

04

2

2

432

32132

6 d)

4 g) )3(6 c)

6

4 f) )2( b)

)2( e))5)(4( a)

y

x

y

axx

xyx

yxmnnm

Try Some Harder Ones4 2

1

33 2

4

3

25

15

2

4

4( )

24( )

x y

x y

x y

y

x y

x y

Scientific Notation

000,000,876,9.4

1054.6.3

00000815.0.2

10468.2.1

7

5

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, , then

2n1

thn

thn

a b b is the n root of a

a b b is the n root of a

n index

a radicand

Examples

45

3

16 .532.4

125

8 .349 .2 49.1

Properties of Radicals

1.

2.

3. 0

4.

5.

6. For even,

For odd,

mn m n

n n n

n

nn

m n mn

nn

n n

n n

a a

a b ab

a ab

bb

a a

a a

n a a

n a a

Let’s Look at Property #6

6. For even,

For odd,

n n

n n

n a a

n a a

Ok… think about this 49 ?

2 49x What are the solutions to

this?

Let’s Try a few

3 6x y

5 24 x y

7 76 x y

4 33 x y

Simplifying RadicalsNo 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

42

87

3 4

3 6

3 4

3

44

3

4

50 .9

48 .8

16 .7

40.6

54.5

24.4

8.3

75.2

48.1

yx

yx

x

x

a

x

x

Adding and Subtracting Radicals

must be “like radicals” (same index and radicand)

Examples

3 43 5416.2

273482.1

xx

Rationalizing Denominators &

Numerators

23

7

3 6

3

Ex. 1

Ex. 2

Ex. 3 (with 2 terms in the denominator)

Ex. 4 (with 2 terms in the numerator)

24

3

2

53

Now You Try Some

3 23

823

493

63

4

x

Rational Exponents

n mmn

mnn

m

nn

aaaa

aa

1

1

.2

.1

Examples

2

3

32

53

32

51

532

3 2

100

1 27

32 8

66xx