Copyright©amberpasillas2010. 1 1 = +1 1 -1 = -1 -1 -1 = +1 -1 -1 -1 = -1 Multiply Integers REVIEW Odd # of Negatives = Negative Even # of Negatives =

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1 • 1 = +1

1 • -1 = -1

-1 • -1 = +1

-1 • -1 • -1 = -1

Multiply Integers REVIEW

Odd # of Negatives = Negative Even # of Negatives = Positive

-1 • -1 • -1 • -1 = +1

-1 • -1 • -1 • -1 • -1 = -1

-1 • -1 • -1 • -1 • -1 • -1 = +1


22 Means… 2 • 2 = 4 21 Means… 2 = 2

20 Means… 1

What does 2-1 Mean?


What does 2-1 Mean? You cannot leave an exponent

negative because there is no way to express it’s meaning.

You must make it positive!

11 1

22


You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals.

2 51

5 2 If the negative

exponent is on top, move it to the bottom.

22

12

2 2

2

12

2 1

4 4

1


Definition of Negative Exponent

For any integer n, a-n is the reciprocal of an

1n

naa




11 1

22




22

1( 5)

( 5)


Simplify.11) 3

23) 5

22) 4

24) 6

13

215

125

214

116

216

136

A negative exponent is an inverse!1x 1

xFlip the number over to make the exponent positive!

1 1

1 1


Follow the Pattern!3323130313

23

33

= 3 3 3= 3 3= 3

= 1

=1

3

=1

3

1

3

=1

3

1

3

1

3

33

3

3

3

3

Notice that anything to the zero power is always one!


Follow the Pattern!

210

10

10

10

10

3

4

5

100

1,00010,000

100,000

10110

110

-1 = 0.1

10-2

1

110 2

1100

= 0.01

10-3 1

10 3 11000 = 0.001


Study the table and FOLLOW THE PATTERN!Exponent, n 25 24 23 22 21 20 2–1 2–2 2–3

Power, 2n 32 16 8 4 2 1 12

14

1 8

What do you think 2–4 will be?2–4 = 1 = 1

24 16


25 32


Study the table and FOLLOW THE PATTERN!Exponent, n 35 34 33 32 31 30 3–1 3–2 3–3

Power, 3n 243 81 27 9 3 1 13

19

1 27


34 81


35 243


Zero Exponent:

Negative Exponent:

0 1a 1n

naa


01) 6 Simplify.

02) -2

03) 9 04) 5 20 8

1 1

1 1

0 1x


Simplify.

11) 2

13) 5

22) 10

34) 2

12

15

21

101

100

312

18

1n

naa

1 1

1 1


1n

naa

25) 12 26) 7 21

121

144

217

149

Simplify.

1 1


Identity Property Why It Works43 3 3 3 3 33 3 3 3 23 3 313 303 1

11

11

32

3-2

9 2

1

3

91

9= 1

Any number to the zero power is ALWAYS ONE.

x0 = 1


Take Out Your Study Guide!!!


Powers of Ten

210

10

10

10

10

3

4

5

100

1,00010,000

100,000

10110

110

-1 = 0.1

# 4

10-2

1

110 2

1100

= 0.01

10-3 1

10 3 11000

= 0.001


Negative Exponents

# 5

EXAMPLES:

232

1

3

4( 5) 4

1

( 5)


1nn

aa

A negative exponent is an inverse!


Any number to the zero power is ALWAYS ONE.

x0 = 1

Ex:

# 6

04 12 25 5 2 25 05 1

03 4 1 1

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Copyright©amberpasillas2010. 1 1 = +1 1 -1 = -1 -1 -1 = +1 -1 -1 -1 = -1 Multiply Integers REVIEW Odd # of Negatives = Negative Even # of Negatives =