Math 10 Name: Unit 2: Roots and Powers (Day 4)

Exponential Notation Cont.

A negative exponent in the denominator becomes a positive exponent in the numerator:

i) 42

1

ii) 26

1

iii) 33

1

iv) 27

1

ex: Rewrite with positive exponents:

i) 263

122

fed

bca ii)

31

2343

ts

rqp

Ex: Use a power with a negative exponent (other than -1) to write an equivalent form for:

i) 81

1 ii)

27

1 iii) 9

I. Rational Exponents

A radical can be changed into a fractional exponent or a fractional exponent can be changed into

as radical as follows:

b

aa

b xx

Examples: Evaluate

i) 3

2

27 ii) 2

5

4

iii) 2

3

16

9

iv) 3

5

)8(

v) 5.036 vi) 6.032

vii) 75.016 viii) 5.064.0

Write each number as a power with exponent 2

1

i) 5 ii) 7

Write in exponential form: nx

i) 5

7 12 ii)

8

2

5

iii)

5

3

2

iv)

3 95

Examples:

i) )7)(5( 243 xyyx ii) 92

45

6

9

yx

yx

iii) 362 )3( yzx

* The power law is always done before the multiplication and division laws *

iv) 322 )2)(5( baab v) 22

3422

)4(

)8)(6(

mn

nmnm

vi) 25

2242

)6(

)2()3(

dc

cddc

II. Combining Negative Exponents and Fractional Exponents

ab

b

ab

a

xx

x11

i) 4

3

16

ii) 3

2

27

iii) 2

3

16

9

iv) 6.032

v) 2

1

25.0

vi) 3

2

064.0

Homework: 1.5 # 6-9odd, 10a-d, 11odd