Warm-UpWarm-UpSimplify

4 minutes

1)

2 2 2

2)

23

3)

(2 2 2) (2 2)

4)

100 1000

4.1 Exponents4.1 ExponentsObjectives: •To multiply numbers in exponential form•To divide numbers in exponential form•To simplify expressions with negative exponents

Multiplying Powers with Like Multiplying Powers with Like BasesBases

For any rational number a, and for all whole numbers m and n,

m n m na a a

Example 1Example 1Simplify. Express using exponents.a) 3 62 2b) 2 4a ac) 5 3z z z

d) 2 3 4 5(x y )(x y )

926a

9z6 8x y

PracticePractice

a) 2 45 5b) 5 3a ac) 2 3 4y y y

d) 2 2 5(mn )(mn )

Simplify. Express using exponents.

Dividing Powers with Like BasesDividing Powers with Like Bases

For any rational number a except 0, and for all whole numbers m and n,

mm n

na aa

Example 2Example 2

5

377

Simplify. Express using exponents.

a)7

3yyb)4 3

2r srsc)

27

4y

3r s

PracticePractice

a)

b)

c)

Simplify. Express using exponents.7

355

3

2hh8 4

3x yxy

Negative ExponentsNegative Exponents

For any rational number a except 0, and for all whole numbers m and n,

mm1a a

Example 3Example 3Express using positive exponents.

16a)

25b)

4xc)

4xyd)

16

215

41x

4xy

PracticePractice

1)

2)

3)

Express using exponents.22

4y

23c

The Exponent ZeroThe Exponent Zero

a0 = 1 for any rational number a except 0.

0a 1

Example 4Example 4Simplify.

24a)

31b)

04c)

0xd)

214

311

1

1

116

1

PracticePractice

1)

2)

3)

Simplify.32

91

03