8.1 Zero & Negative Exponents. 8.1 – Zero & Negative Exponents Goals / “I can…” ...

8.1

Zero & Negative Exponents

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

Goals / “I can…”Simplify expressions with zero and negative

exponentsEvaluate exponential expressions

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

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

22 Means… 2 • 2 = 4 21 Means… 2 = 2

20 Means… 1

What does 2-1 Mean?

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

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

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

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

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an

1n

naa

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an

11 1

22

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an

22

1( 5)

( 5)

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

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

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

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

8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents

Zero Exponent:

Negative Exponent:

0 1a 1n

naa

RULE: YOU SHOULD NEVERNEVER HAVE A NEGATIVE EXPONENT AS YOUR FINAL

ANSWER

8.1 – Zero & Negative Exponents

01) 6

Simplify.

02) -2

03) 9 04) 5 20 8

1 1

1 1

0 1x

8.1 – Zero & Negative Exponents

8.1 – Zero & Negative Exponents

Simplify the following:

a. 3 c. (-4)

b. (-8.1) d. (2.45678913)

-2 -5

0 0

1n

naa

25) 12 26) 7 21

121

144

217

149

Simplify.

1 1

8.1 – Zero & Negative Exponents

8.1 – Zero & Negative Exponents

Simplify

a. 11m b. 7s - 4t

c. d.

-5 2

3

2a

2

5

v

n

Simplify the following expressions:

2

3

5

0

4

1.4

.3

1.2

6.1

gh

x

7

4

5

0

6

3

.8

7.

0) zfor (.6

.5

t

r

xy

z

p

n

3h

g

1

x5

16

-n3p6

1

55

1

yx

4

7

r

t

Practice Problems

1. 2-2

¼

2. (-2)0

1

3. 5-x

1/5x

4. (½)-1 2

5. 5(2-1)5/2

6. 2x-2y-3

2/y3x2

More Practice

7. x-5

1/x5

8.

x5/2

9. x4y-7

x4/y7

10.

x3y/9

521

x

1391

yx

8.1 – Zero & Negative Exponents

Evaluate each expression for n = -2 and w = 5

a. n w b. c. d. 2

1

w

n

4

0

n

w2

1nw

-3 0