The Laws of Exponents revised edition.ppt

to discuss the laws of exponent

2. ExponentsExponents

3
5Power
base
exponent
3 3
means that is the exponential
form of t
Example:
he number
125 5 5
.125

5
3
means 3 factors of 5 or 5 x 5 x 5

3. The Laws of Exponents:The Laws of Exponents:
Exponential form: The exponent of a power indicates
how many times the base multiplies itself.
n
n times
x xxx xxxx

 

3
Example: 5 555 
n factors of x

4. #1: Multiplying Powers (Product of Powers): If
you are multiplying Powers with the same base, KEEP the BASE
& ADD the EXPONENTS!
m n m n
x x x

 
So, I get it!
When you
multiply
Powers, you
add the
exponents!
512
2222
93636




5. #2: Dividing Powers (Quotient of Powers):
When dividing Powers with the same base, KEEP the BASE &
SUBTRACT the EXPONENTS!
m
m n m n
n
x
x x x
x

  
So, I get it!
When you
divide
Powers, you
subtract the
exponents!
16
22
2
2
426
2
6




6. Try these:

22
33.1

42
55.2

25
.3 aa

4
12
.7
s
s

5
9
3
3
.8

44
812
.9
ts
ts

7. 
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 


8. 
4
12
.7
s
s

5
9
3
3
.8

44
812
.9
ts
ts

54
85
4
36
.10
ba
ba
SOLUTIONS
8412
ss

8133
459


4848412
tsts 

35845
9436 abba 


9. #3: Power of a Power: If you are raising a Power to an
exponent, you multiply the exponents!

n
m mn
x x
So, when I
take a Power
to a power, I
multiply the
exponents
62323
55)5( 


10. #5: Product Law of Exponents: If the product of the
bases is powered by the same exponent, then the result is a
multiplication of individual factors of the product, each powered
by the given exponent.

n
n n
xy x y 
So, when I take
a Power of a
Product, I apply
the exponent to
all factors of
the product.
222
)( baab

11. #6: Quotient Law of Exponents: If the quotient of the
bases is powered by the same exponent, then the result is both
numerator and denominator , each powered by the given exponent.
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
2
4
4
4







12. Try these:

5
2
3.1

4
3
.2a

3
2
2.3a

13. 
5
2
3.1

4
3
.2a

3
2
2.3a
 
2
352
2.4 ba

22
)3(.5a

3
42
.6ts
SOLUTIONS
10
3
12
a
6323
82 aa

6106104232522
1622 bababa 


4222
93 aa

1263432
tsts 


14. 





5
.7
t
s









2
5
9
3
3
.8









2
4
8
.9
rt
st









2
54
85
4
36
10
ba
ba
SOLUTIONS

622322
2
3
8199 babaab 

2
82
2
4
r
ts
r
st










8
2
4
33
5
5
t
s

15. #4: Negative Law of Exponents: If the base is powered
by the negative exponent, then the base becomes reciprocal with the
positive exponent.
1
m
m
x
x


So, when I have a
Negative Exponent, I
switch the base to its
reciprocal with a
Positive Exponent.
Ha Ha!
If the base with the
negative exponent is in
the denominator, it
moves to the
numerator to lose its
negative sign!
93
3
1
125
1
5
1
5
2
2
3
3




and

16. #5: Zero Law of Exponents: Any base powered by zero
exponent equals one.
0
1x
1)5(
1
15
0
0
0



a
and
a
and
So zero
factors of a
base equals 1.
That makes
sense! Every
power has a
coefficient
of 1.

17. Try these:

0
2
2.1 ba

0
42
.6 ts

18. SOLUTIONS

0
2
2.1 ba

1
5
.3a

 72
4.4 ss
 


4
32
3.5 yx

0
42
.6ts
1
5
1
a
5
4s
 
12
8
1284
81
3
y
x
yx 

1

19. 








1
2
2
.7
x









2
5
9
3
3
.8









2
44
22
.9
ts
ts









2
54
5
4
36
.10
ba
a
SOLUTIONS
4
4
1
x
x








8
8
2
4
3
1
33 



44
2
22
tsts 


2
10
1022
81
9
a
b
ba 
