warm up exercise… find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x)...

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Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1

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2 2 Means… 2 2 = Means… 2 = Means… 1 What does 2 -1 Mean? 8.1 – Zero & Negative Exponents

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Page 1: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

Warm Up Exercise…Find the range of the function with the

given domain (x) – {-2, 0, 3.5}f(x) = (-2x)(-2x)

g(x) = 10 – (x)(x)(x)

y = 5x – 1

Page 2: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

Lesson #8.1

Zero & Negative Exponents

SWBAT simplify expressions with zero and negative exponents; evaluate exponential

expressions.

Concept: UNIT 8

Page 3: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

Page 4: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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 12

2

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

Page 5: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

2 5 15 2 If the negative exponent

is on top, move it to the bottom.

22

122

22

1 22 1

4 4

1

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

Page 6: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

Page 7: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

11 12

2

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

Page 8: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

Page 9: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

Page 10: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

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

Page 11: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

01) 6

Simplify.

02) -2

03) 9 04) 5 20 8

1 1

1 1

0 1x

8.1 – Zero & Negative Exponents

Page 12: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

8.1 – Zero & Negative Exponents

Simplify the following:a. 3 c. (-4)

b. (-8.1) d. (2.45678913)

-2 -5

0 0

Page 13: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

1n

naa

25) 12 26) 7 21

121

1442

17

149

Simplify.

1 1

8.1 – Zero & Negative Exponents

Page 14: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

8.1 – Zero & Negative Exponents

Simplifya. 11m b. 7s - 4t

c. d.

-5 2

3

2a 2

5

vn

Page 15: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

Simplify the following expressions:

2

3

5

0

41.4

.3

1.2

6.1

ghx

7

4

5

0

6

3

.8

7.

0) zfor (.6

.5

tr

xy

z

pn

3hg

1

x5

16

-n3p6

1

55

1yx

4

7

rt

Page 16: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

Practice Problems

1. 2-2

¼

2. (-2)0

13. 5-x

1/5x

4. (½)-1 2

5. 5(2-1)5/2

6. 2x-2y-3

2/y3x2

Page 17: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

More Practice

7. x-5

1/x5 8.

x5/29. x4y-7

x4/y7

10.

x3y/9

521

x

1391

yx

Page 18: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

8.1 – Zero & Negative Exponents

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

a. n w b. c. d. 2

1

wn

4

0

nw

2

1nw

-3 0