PPT: Laws of Exponents
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Transcript PPT: Laws of Exponents
Exponents
Power
5
exponent
3
base
Example: 125 53 means that 53 is the exponential
form of the number 125.
53 means 3 factors of 5 or 5 x 5 x 5
The Laws of Exponents:
#1: Exponential form: The exponent of a power indicates
how many times the base multiplies itself.
x x x x x x x x
n
n times
n factors of x
Example: 5 5 5 5
3
#2: Multiplying Powers:
If you are multiplying Powers
with the same base, KEEP the BASE & ADD the EXPONENTS!
x x x
m
So, I get it!
When you
multiply
Powers, you
add the
exponents!
n
m n
2 2 2
6
3
63
2
9
512
#3: Dividing Powers: When dividing Powers with the
same base, KEEP the BASE & SUBTRACT the EXPONENTS!
m
x
m
n
mn
x
x
x
n
x
So, I get it!
When you
divide
Powers, you
subtract the
exponents!
6
2
6 2
4
2
2
22
16
Try these:
12
1. 3 3
2
2
7.
2. 52 54
8.
3. a a
5
2
4. 2s 4s
2
7
12 8
9.
5. (3) (3)
2
3
6. s t s t
2 4
7 3
s
4
s
9
3
5
3
s t
4 4
st
5 8
10.
36a b
4 5
4a b
SOLUTIONS
2 2
4
5 2
a
1. 3 3 3 3 81
2 4
6
2
4
2. 5 5 5 5
2
2
3. a a a
5
2
4. 2s 4s 2 4 s
2
7
5. (3) (3) (3)
2
3
6. s t s t
2 4
7 3
s
7
2 7
2 3
8s
(3) 243
2 7 43
t
9
5
s t
9 7
SOLUTIONS
12
7.
8.
9.
10.
s
12 4
8
s
s
4
s
9
3
9 5
4
3
3
81
5
3
12 8
s t
12 4 8 4
8 4
s
t
s
t
4 4
st
5 8
36a b
5 4 8 5
3
36
4
a
b
9
ab
4 5
4a b
#4: Power of a Power: If you are raising a Power to an
exponent, you multiply the exponents!
x
n
m
So, when I
take a Power
to a power, I
multiply the
exponents
x
mn
32
(5 ) 5
3
2
5
5
#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.
xy
So, when I take
a Power of a
Product, I apply
the exponent to
all factors of
the product.
n
x y
n
n
(ab) a b
2
2
2
#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
x
x
n
y
y
So, when I take a
Power of a
Quotient, I apply
the exponent to
all parts of the
quotient.
n
4
2 2 16
4
81
3 3
4
Try these:
5
2 5
1. 3
3. 2a
4. 2 a b
2. a
s
7.
t 2
39
8. 5
3
3 4
2 3
2
5 3 2
5. (3a )
2 2
2 4 3
6. s t
2
st
9. 4
rt
5 8 2
36a b
10.
4 5
4a b
8
SOLUTIONS
2 5
1. 3
2. a
3 4
10
3
a12
2a
3. 2a
2
2 3
3
5 3 2
4. 2 a b
23
8a
6
22 52 32
4 10 6
10 6
2
a
b
2
a
b
16
a
b
5. (3a ) 3 a 22 9a 4
2
2 2
2 4 3
6. s t
23 43
s t
s t
6 12
SOLUTIONS
5
s
7.
t
5
s
5
t
2
3
8. 5 34
3
9
2
3
8
2
4 2
2 8
st
st
s
t
9. 4
2
r
rt
r
8
36a b
10
4 5
4
a
b
5 8
2
9ab
3 2
92 a 2b32 81a 2b6
#7: Negative Law of Exponents: If the base is powered
by the negative exponent, then the base becomes reciprocal with the
positive exponent.
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!
x
m
1
m
x
1
1
5 3
5
125
and
3
1
2
3
9
2
3
#8: Zero Law of Exponents: Any base powered by zero
exponent equals one.
x 1
0
So zero
factors of a
base equals 1.
That makes
sense! Every
power has a
coefficient
of 1.
50 1
and
a0 1
and
(5 a ) 0 1
Try these:
1.
2a b
0
2
y 2 y 4
2.
a
5 1
3.
2
4. s 4s
7
s t
2
5. 3x y
6.
3 4
2 4 0
1
2
7.
x 2
39
8. 5
3
2
2
s t
9. 4 4
s t
2
5
36a
10. 4 5
4a b
2 2
SOLUTIONS
0
1. 2a b 1
2
1
3. a
5
a
5
2
7
4. s 4s 4s
5 1
2
5. 3x y
2 4 0
6. s t
3 4
3 x y
1
4
8
12
8
x
81y12
SOLUTIONS
1
2
7.
x
9 2
3
8. 5
3
2
1
x
4
4
x
3
2
4 2
1
3 8
3
8
s t
2 2 2
4 4
s t
9. 4 4 s t
s t
10
2
5
b
2
2
10
36a
9
a
b
2
10. 4 5
81a
4
a
b
2 2