I hereby present a PPT on The Laws of Exponents. This PPT is from the chapter Exponent and Powers. Thank You!!

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

3. The Laws of Exponents:
#1: Exponential form: The exponent of a power indicates
how many times the base multiplies itself.
n
n times
x x x x x x x x

      1 4 44 2 4 4 43
3
Example: 5 5 5 5  
n factors of x

4. #2: Multiplying 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. #3: Dividing 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
 72
42.4 ss
 32
)3()3(.5
 3742
.6 tsts
4
12
.7
s
s
5
9
3
3
.8
44
812
.9
ts
ts
54
85
4
36
.10
ba
ba

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. #4: Power of a Power: If you are raising a Power to an
exponent, you multiply the exponents!
 
nm mn
x x
So, when I
take a Power
to a power, I
multiply the
exponents
52323
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
44







12. Try these:
  
52
3.1
  
43
.2 a
  
32
2.3 a
  
2352
2.4 ba
 22
)3(.5 a
  
342
.6 ts






5
.7
t
s






2
5
9
3
3
.8






2
4
8
.9
rt
st






2
54
85
4
36
.10
ba
ba

13.   
52
3.1
  
43
.2 a
  
32
2.3 a
  
2352
2.4 ba
 22
)3(.5 a
  
342
.6 ts
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
  62232223
8199 babaab  
2
8224
r
ts
r
st






  824
33 
5
5
t
s

15. #7: Negative Law of Exponents: If the base is powered
by the negative exponent, then the base becomes reciprocal with the
positive exponent.
1m
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. #8: 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:
  
02
2.1 ba
 42
.2 yy
  
15
.3 a
 72
4.4 ss
  
 432
3.5 yx
  
042
.6 ts






12
2
.7
x






2
5
9
3
3
.8






2
44
22
.9
ts
ts






2
54
5
4
36
.10
ba
a

18. SOLUTIONS
  
02
2.1 ba
  
15
.3 a
 72
4.4 ss
  
 432
3.5 yx
  
042
.6 ts
1
5
1
a
5
4s
  12
8
1284
81
3
y
x
yx 
1

19. 





12
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
824
3
1
33  
  44222
tsts 

2
10
1022
81
9
a
b
ba 