negative exponents
DESCRIPTION
Negative Exponents. and. Zero Exponents. Negative & Zero Exponents. Multiply Integers REVIEW. = + 1. 1 • 1. 1 • -1. = - 1. -1 • -1. = + 1. -1 • -1 • -1. = - 1. -1 • -1 • -1 • -1. = + 1. -1 • -1 • -1 • -1 • -1. = - 1. -1 • -1 • -1 • -1 • -1 • -1. = + 1. - PowerPoint PPT PresentationTRANSCRIPT
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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
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22 Means… 2 • 2 = 4 21 Means… 2 = 2
20 Means… 1
What does 2-1 Mean?
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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
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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
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Definition of Negative Exponent
For any integer n, a-n is the reciprocal of an
1n
naa
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Definition of Negative Exponent
For any integer n, a-n is the reciprocal of an
11 1
22
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Definition of Negative Exponent
For any integer n, a-n is the reciprocal of an
22
1( 5)
( 5)
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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
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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!
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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
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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
What do you think 2–5 will be?2–5 = 1 = 1
25 32
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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
What do you think 3–4 will be?3–4 = 1 = 1
34 81
What do you think 3–5 will be?3–5 = 1 = 1
35 243
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Zero Exponent:
Negative Exponent:
0 1a 1n
naa
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01) 6 Simplify.
02) -2
03) 9 04) 5 20 8
1 1
1 1
0 1x
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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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1n
naa
25) 12 26) 7 21
121
144
217
149
Simplify.
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
32
3-2
9 2
1
3
91
9= 1
Any number to the zero power is ALWAYS ONE.
x0 = 1
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Take Out Your Study Guide!!!
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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
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Negative Exponents
# 5
EXAMPLES:
232
1
3
4( 5) 4
1
( 5)
For any integer n, a-n is the reciprocal of an
1nn
aa
A negative exponent is an inverse!
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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