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copyright©amberpasillas2010
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.
copyright©amberpasillas2010
An exponent is written in exponential form when it is simplified using exponents.
32a
3Exponential Form
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32a
3
An exponent is written in factor form when it is written out.
= 3•3•a•a•a
Factor Form
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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
copyright©amberpasillas2010
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
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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.
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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
If the negative exponent is on bottom, move it to the top.
22
12
2 1
4 4
1
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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
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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!
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Just flip the fraction over to make the exponent positive!
213
225
231
9
252
254
3 31 1
5 52 2
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Just flip the fraction over to make the exponent positive!
245
223
254
2516
232
94
5 54 4
3 32 2
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Just flip the fraction over to make the exponent positive!
31
4
215
341
64 641
251
25 251
4 4 41 1 1
5 5
1 1
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Rewrite so there is NO negative exponent.
41) n 3 52) a b 4
1n
3 51=
a b
HINT: Think backwards!
1 1
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Rewrite so there is NO negative exponent.3 03) m n
31 1
m
31
m
44) 3x
413x
4
3x
1 1
HINT: Think backwards!
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Rewrite so there is NO negative exponent. 4
5) 2a
41
2a 4
116a
2•2•2•2 = 16
1
HINT: Think backwards!
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Rewrite so there is NO negative exponent.
26) 4a 21a
4 24
a
1
HINT: Think backwards!
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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
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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
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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.
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Rewrite so there is a negative exponent.
711) n 5
12) k7n 5k
HINT: Think backwards!
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Rewrite so there is a negative exponent.
393) x
39 x 39x
14) t
1t
HINT: Think backwards!
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Rewrite so there is a negative exponent.
55) x0
86) x
51
x 81
11
81
HINT: Think backwards!
copyright©amberpasillas2010
Rewrite so there is a negative exponent.
711) n 5
12) k7n 5k
HINT: Think backwards!
copyright©amberpasillas2010
Rewrite so there is a negative exponent.
393) x
39 x 39x
14) t
1t
HINT: Think backwards!
copyright©amberpasillas2010
Rewrite so there is a negative exponent.
55) x0
86) x
51
x 81
11
81
HINT: Think backwards!