Dec 24, 2015
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
The Laws Of Exponents
The laws of exponents tell us how to simplify expressions involving exponents.
There are 7 laws of exponents.
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
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?
Write in standard form.
Write in exponential form.
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
The Laws of Exponents:The Laws of Exponents:
#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
Try these:
22 33.1
42 55.2
25.3 aa
72 42.4 ss
32 )3()3(.5
3742.6 tsts
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
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.
#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
Try these:
4
12
.7s
s
5
9
3
3.8
44
812
.9ts
ts
54
85
4
36.10
ba
ba
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
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.
#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(
Try these:
523.1
43.2 a
523.1
43.2 a
SOLUTIONS
10312a
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.
#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
Try these:
322.3 a
23522.4 ba
22 )3(.5 a
342.6 ts
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
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.
#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
Try these:
5
.7t
s
2
5
9
3
3.8
2
4
8
.9rt
st
2
54
85
4
36.10
ba
ba
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
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.
#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
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
SOLUTIONS
15.3 a
72 4.4 ss
4323.5 yx
5
1
a54s
12
81284
813
y
xyx
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
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.
#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!
Try these:
022.1 ba
042.6 ts
SOLUTIONS
022.1 ba
042.6 ts
1
1
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.