Copyright©amberpasillas2010. For Learning to Happen: Remove all other thoughts from your mind. This...


For Learning to Happen:•Remove all other thoughts from your mind.•This lesson is a challenge so please follow along with what I am teaching you.•Pay close attention to this lesson.•Try all of the examples.•Ignore all other distractions.


An exponent is written in exponential form when it is simplified using exponents.

32a

3Exponential Form


32a

3

An exponent is written in factor form when it is written out.

= 3•3•a•a•a

Factor Form


= 2 • 2 • 2 • 2 • 22

48

16

5

32

How to Multiply Out Exponents


When simplifying exponents you must watch the sign and the parenthesis!

52

= 5•5 = 25

–52

= – (5)•(5) = –25

(-5)2

=(-5)(-5) = 25 –(5)2

= - (5)(5) = –251

1


Simplify.

01) 18 02) -3

03) 5 04) 2 3 1

1 1

1 1

0x 1

(1) 0(6 1)0(5)


4a a a a a 3a a a a 2a a a1a a0a 1

aa

aa

Here is why any number to the zero power is 1.

PositiveExponents

RepetitiveMultiplication

Identity Property: Any number multiplied by one equals itself.

11

11


4a a a a a 3a a a a 2a a a1a a0a 1

aa

aa

Here is why any number to the zero power is 1.

PositiveExponents

RepetitiveMultiplication

11

11

a0 = 1 Notice there are zero “a’s” present.

However, there is still a one because of the Identity Property.


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

If the negative exponent is on bottom, move it to the top.

22

12

2 1

4 4

1


Simplify.11) 4

23) 10

32) 2

24) 6

14

21

101

100

312

18

216

136

A negative exponent is an inverse!1x 1

xFlip the number over to make the exponent positive!

1 1

1 1


41) 2 22) 5

53) 2 24) 9

412 2

15

512

132

219

181

116

125

1 1

1 1


0a 11a 1

a2a

21a

3a

a

a

a

31a

NegativeExponents

Repetitive Division

A negative exponent is an inverse!

Follow the pattern for Negative Exponents!


21

5

Just flip the fraction over to make the exponent positive!

25

1



213

225

231

9

252

254

3 31 1

5 52 2



245

223

254

2516

232

94

5 54 4

3 32 2



31

4

215

341

64 641

251

25 251

4 4 41 1 1

5 5

1 1


Rewrite so there is NO negative exponent.

41) n 3 52) a b 4

1n

3 51=

a b

HINT: Think backwards!

1 1


Rewrite so there is NO negative exponent.3 03) m n

31 1

m

31

m

44) 3x

413x

4

3x

1 1



Rewrite so there is NO negative exponent. 4

5) 2a

41

2a 4

116a

2•2•2•2 = 16

1



Rewrite so there is NO negative exponent.

26) 4a 21a

4 24

a

1



Take Out Your Study Guide!!!


Exponents and Parenthesis

#7Factored Form

8 • x • x • xExponential Form

8x3

4(xy)(xy) 4(xy)2

(8x)3 (8x)(8x)(8x) = 8

3x

3

= 4 x2y

2

(5x3)

2 (5 x x x)(5 x x x) = 25x6

(2y2z)

2 (2 y y z) (2 y y z) = 22y

4z

2

= 512x3

= 52(x

3)2

= 4y4z

2


Fractions With Exponents

311) 2

222) 3

214) 3

225) 5

26) 9

12 2 2

2 23 3

231

9

252

254

219

181

18

49

# 8

213) 5

1 15 5 1

25


Negative Exponent Examples51) n

3 42) a b

44) 3a

45) 3a

26) 5x 3 03) m n

51n

3 41=

a b

413a

43a

41

3a 4

181a

215x

25

x

31 1

m

# 9

31

m

EXTRAS: You can use these extra slides if you are taking a

positive exponent and writing it as a negative exponent.



Rewrite so there is a negative exponent.

711) n 5

12) k7n 5k




393) x

39 x 39x

14) t

1t




55) x0

86) x

51

x 81

11

81




711) n 5

12) k7n 5k




393) x

39 x 39x

14) t

1t




55) x0

86) x

51

x 81

11

81



21

8


28

1

2

2

8

1

#?

64

24

7

27

4

2

2

7

4 49

16

31

4

34

1

3

3

4

( 1)

64

1

64

Copyright©amberpasillas2010. For Learning to Happen: Remove all other thoughts from your mind. This...

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