Transcript Document
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 =1
x × 44
x × x4
××××x
× x × x3
×x
2444
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:
s
3.
=
4
s
12
1. 3 3
2
2
2. s t ´ s t =
2 4
7 3
36a b
4.
=
4 5
4a b
5 8
SOLUTIONS
2 2
1. 3 3 3
2
2
2. s t ´ s t =
2 4
7 3
s
3 81
4
2 7 43
t
s t
9 7
s
12 4
8
3.
= s
s
4
s
5 8
5 4 8 5
3
36a b
36
4
a
b
9
ab
4.
=
4 5
4a b
12
#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:
2 5
1. 3
2. ( s t
æsö
3. ç ÷ =
ètø
5
)
2 4 3
=
æ 36a b ö
4. ç 4 5 ÷ =
è 4a b ø
5 8 2
SOLUTIONS
2 5
2. ( s t
)
1. 3
2 4 3
10
3
= s 23t 43 s 6t12
æsö
3. ç ÷ =
ètø
5
5
s
5
t
æ 36a 5b8 ö
4. ç 4 5 ÷ = 9ab3
è 4a b ø
2
2
2 32
9 a b
2
81a b
2 6
#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
Homework
• Page 88, #2-11
• Page 89, #16-21
• Page 90, #22-25, 27-30