7-1 Zero and Negative Exponents

Use your calculator to complete the following table keeping answers as positive powers of 2.

In General: is the of .

FRACTION

RECIPROCAL

32 22 12 02 12 22 32 42

8 4 2 11

2

1

4

1

8

1

16

2 n 2n

Negative Exponent Property:

For any nonzero numbers b and all n,

Zero Exponent Property:

For any nonzero number a,

1nn

bb

0 1a

Examples:

2.) 3a

1.) Write each as a simple fraction without negative exponents.

3.) 5b 1.) 8c 4.) 10d

2

1 1

3 9

3

1 1

5 125

1

1 1

8 8 4

1 1

10 10,000

Examples:

1.)

5a

2.) Write each fraction as a power of an integer.

1.)

27b

1.)

16c

4.)

25d

11

15

5 3

3

13

3 4

2 4

1 12

4 2

22 2

2

22 5

5

Examples:

0.) 12a

3.) Simplify each of the following.

0.) 6b 0.) 0c 0

.) 7d x

1 1 1 1

Simplifying Exponential Expressions:

An algebraic expression is in simplest form when powers with a variable base are written with onlyexponents.

POSITIVE

Rewrite the following using only positive exponents:

4.) a m4

1.) by

2 4.) 3c a b 5 3.) d x y

4

1 m

4

4

11

y

y

2 4

3 a b

5

3 x

y

Evaluating an Exponential Expression:

Simplify the exponential expression substituting the values for the variables.

BEFORE

Evaluate each expression for a = 2 and b = -4

3 1.) a a b 4 2.) 2b a b 3 0.) 2c a b

3 32 8= = 2

4 4

a

b

22

4 4

2 42 32= = 2

2 16

b

a

3 3

2 2 2 1 = = =

2 8 4a

Homework: Sect. 7.1 p. 446-447 #’s 10-44 even