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Talk to your partner: What is a general rule for the

value of any number raised to the zero power: a0 =

0 1a

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01) 6 Simplify.

02) -2

03) 9

1 1

1 1

0 1x

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You do NOT want to have negative exponents in your answer. An expression is NOT simplified when there is a negative exponent.

Turn and Talk:

What is a general rule for the value of any number to a negative power? a-x =

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MEMORIZE this saying….“JUMP the LINE

&CHANGE the EXPONENT’S SIGN”

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Definition of Negative Exponent

For any integer n, a-n is the reciprocal of an 1

nna

a

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Definition of Negative Exponent

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

11 12

2

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Definition of Negative Exponent

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

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Remember the saying….“JUMP the LINE

&CHANGE the EXPONENT’S SIGN”

And think about the next slide….

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What if the negative exponent is in the denominator?

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Simplify.11) 3

23) 5 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

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Follow the Pattern!2

1010101010

3

4

5

100

1,00010,000

100,000

10110

110

-1 = 0.1

10-2

1

110 2

1100 = 0.01

10-3 110 3

11000 = 0.001

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Zero Exponent:

Negative Exponent:

0 1a 1

nna

a

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Simplify.

11) 2

13) 5

22) 10

34) 2

12

15

21

101

100

312

18

1n

naa

1 1

1 1

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

11

11

3 2 3 -2

9 2

13

919 = 1

Any number to the zero power is ALWAYS ONE.

x0 = 1