exponents exponential form base exponent 53 53 means the product of 3 factors of 5 = 5 x 5 x 5
TRANSCRIPT
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ExponentsExponents
35ExponentialForm
base
exponent
3 3 means that is the exponential
form of t
Example:
he number
125 5 5
.125
53 means the product of 3 factors of 5 = 5 x 5 x 5
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The Laws Of Exponents
The laws of exponents tell us how to simplify expressions involving exponents.
There are 7 laws of exponents.
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Exponential form: raising a base to a power stands for repeated multiplication of the base times itself.
n
n times
x x x x x x x x
3Example: 5 5 5 5
n factors of x
Standard formExponential form
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QuestionsWhat is a power?What is a base?What is exponential form?What is standard form?What are the laws of exponents?How many laws of exponents are there?
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Write in standard form.
Write in exponential form.
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Give an example of a power.Give an example of a base.Give an example of exponential form.Give an example of standard form.
Questions
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The Laws of Exponents:The Laws of Exponents:
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#1: Multiplying Bases: If you are multiplying bases with the same base, KEEP the BASE & ADD the EXPONENTS!
m n m nx x x
So, I get it! When you multiply bases, you add the exponents!
512
2222 93636
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Try these:
22 33.1
42 55.2
25.3 aa
72 42.4 ss
32 )3()3(.5
3742.6 tsts
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22 33.1 42 55.2 25.3 aa
72 42.4 ss
32 )3()3(.5
3742.6 tsts
8133 422
725 aa
972 842 ss
SOLUTIONS
642 55
243)3()3( 532
793472 tsts
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QuestionsWhat is the first law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.
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#3: Dividing Bases: When dividing bases with the same base, KEEP the BASE & SUBTRACT the EXPONENTS!
mm n m n
n
xx x x
x
So, I get it!
When you divide bases, you subtract the exponents!
16
222
2 4262
6
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Try these:
4
12
.7s
s
5
9
3
3.8
44
812
.9ts
ts
54
85
4
36.10
ba
ba
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4
12
.7s
s
5
9
3
3.8
44
812
.9ts
ts
54
85
4
36.10
ba
ba
SOLUTIONS
8412 ss
8133 459
4848412 tsts
35845 9436 abba
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QuestionsWhat is the second law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.
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#3: Power of a Power: If you are raising a power to a power, you multiply the exponents!
nm mnx x
So, when I take a Power to a power, I multiply the exponents
62323 55)5(
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Try these:
523.1
43.2 a
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523.1
43.2 a
SOLUTIONS
10312a
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QuestionsWhat is the third law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.
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#4: Product Rule of Exponents: Raising a product to a power means raising all of the factors to the power and then multiplying.
n n nxy x y So, the power of the product is the product of the powers.
222)( baab
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Try these:
322.3 a
23522.4 ba
22 )3(.5 a
342.6 ts
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322.3 a
23522.4 ba
22 )3(.5 a
342.6 ts
SOLUTIONS
6323 82 aa
6106104232522 1622 bababa
4222 93 aa
1263432 tsts
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QuestionsWhat is the fourth law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.
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#5: Quotient Rule of Exponents: Raising a quotient to a power means raising the numerator and denominator to the power.
n n
n
x x
y y
So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient.
81
16
3
2
3
24
44
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Try these:
5
.7t
s
2
5
9
3
3.8
2
4
8
.9rt
st
2
54
85
4
36.10
ba
ba
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5
.7t
s
2
5
9
3
3.8
2
4
8
.9rt
st
2
54
85
4
3610
ba
ba
SOLUTIONS
62232223 8199 babaab
2
8224
r
ts
r
st
824 33
5
5
t
s
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QuestionsWhat is the fifth law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.
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#6: Law of Negative Exponents: A base raised to a negative power is the reciprocal of the base to the positive power.
1mm
xx
So, when I have a negative exponent, I take the reciprocal and change the power to a positive.
933
1
125
1
5
15
22
33
and
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Try these:
42.2 yy
15.3 a
72 4.4 ss
4323.5 yx
122
.7x
2
5
9
3
3.8
2
44
22
.9ts
ts
2
54
5
4
36.10
ba
a
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SOLUTIONS
15.3 a
72 4.4 ss
4323.5 yx
5
1
a54s
12
81284
813
y
xyx
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122
.7x
2
5
9
3
3.8
2
44
22
.9ts
ts
2
54
5
4
36.10
ba
a
SOLUTIONS
4
41x
x
8
824
3
133
44222 tsts
2
101022
819
a
bba
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QuestionsWhat is the sixth law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.
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#7: Zero as an exponent: Anything to the zero power is 1.
0 1x
1)5(
1
15
0
0
0
a
and
a
and
So whenever I raise anything to the zero power it is always 1!
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Try these:
022.1 ba
042.6 ts
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SOLUTIONS
022.1 ba
042.6 ts
1
1
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QuestionsWhat is the seventh law of exponents?When can I use it?When can I not use it?Give an example of where I use it.Give an example of where I can’t use it.Why does it work? Give an example.