Download Chapter 3 Powers and Exponents Section 3.1 Using Exponents to


Chapter
3
Powers
and
Exponents
Section
3.1
Using
Exponents
to
Describe
Numbers
Exponents
are
used
to
write
repeated
multiplications
by
the
same
number
in
a
more
compact
form.
Eg.)
5x5x5x5
=
54
54
is
in
exponential
form,
where
5
is
the
base
(the
number
being
multiplied
by
itself)
and
4
is
the
exponent
–
tells
you
the
number
of
times
you
multiply
the
base
by
itself.
54
is
loosely
called
a
power
(a
base
and
a
power).
It
is
often
read
in
several
ways:
5
to
the
fourth
5
to
the
fourth
power
5
to
the
exponent
four
Some
common
forms:
32
(three
squared)
1)
3
3x3=9
3
(two
cubed)
2)
2
2
2
2x2x2=8
3)
54
on
a
calculator:
5
yx
4
=
625
(standard
form)
4)
Some
can
be
written
36
=
(3x3)
x(3x3)
x
(3x3)
=
9
X
9
X
9
=
93
=
729
OR
(3X3X3)
X
(3X3X3)
=
27
X
27
=
272
=
729
Powers
with
negative
bases:
Eg
#1)
(‐2)4
–
base
is
negative
(‐2)(‐2)(‐2)(‐2)
=
+16
‐
positive
answer
because
there
are
an
even
amount
of
negatives.
Eg
#2)
‐24
‐
without
the
bracket,
only
the
2
is
the
base.
‐
(2)(2)(2)(2)
=
(‐16)
↑
treat
this
as
a
(‐1)
and
multiply
Eg
#3)
(‐2)3
=
(‐2)(‐2)(‐2)
=
(‐8)
–
negative
because
there’s
an
odd
number
for
an
exponent.
*Note:
the
exponent
only
applies
to
the
base,
which
is
the
fist
number
at
it’s
left,
or
what
is
in
the
brackets.
‐(‐5)6
‐
base
is
(‐5)
,
but
not
the
negative
in
front.
=
‐
(‐5)(‐5)(‐5)(‐5)(‐5)(‐5)
=
‐
(+15625)
=
‐15,625
Prime
Factorization:
36
6
6
2
3
2
3
Section
3.2
Exponent
Laws
Factored
form
is
another
name
for
repeated
multiplication.
1.)
am
x
an
=
am+n
**when
multiplying
same
base,
add
exponents.
Eg)
22
x
23
=
25
(2x2)(2x2x2)=25
m
2)
am
÷
an
or
a a n
=
am‐n
**when
dividing
same
bases,
subtract
exponents.
Eg)
24
÷
22
=
22
or
2x2x2x2
=
22
2x2
€
3)
(am)n
=
amxn
**when
a
power
with
an
exponent
is
raised
(taken)
to
another
€
power,
multiply
exponents.
Eg)
(22)3
=
(22)(22)(22)
=
(2x2)(2x2)(2x2)
=
26
4)
(ab)m
=
ambm
**
when
a
product
(multiplied
together)
is
raised
to
a
power,
the
power
applies
to
each
factor
separately.
Eg)
(‐2x3)3
=
(‐2x3)(‐2x3)(‐2x3)
=
(‐2x‐2x‐2)(3x3x3)
=
(‐2)3(3)3
=
‐8(27)
=
‐216
5)
(a/b)n
=
an/bn
**where
a
quotient
(division)
is
raised
to
a
power,
rewrite
with
the
exponent
in
each
place.**b
cannot
equal
0.
Eg)
(2/3)3
=
23/33
=
(2/3)(2/3)(2/3)
=
23/33
=
8/27
6)
a0
=
1
**
always
equals
1,
except
a
cannot
equal
0
Eg)
103
=
1000
102
=
100
101
=
10
100
=
1
Section
3.3
Order
of
Operations
Terminology
Coefficient
–
is
a
number
that
multiplies
an
expression.
(This
can
be
another
number
or
variable.)
This
needs
to
include
the
sign.
Eg
#1)
‐3(4)2
Coefficient
=
‐3
Eg
#2)
‐3x4
Coefficient
=
‐3
Eg
#3)
5x2y4
Coefficient
=
5
Eg
#4)
(‐2)2
Coefficient
=
1
(multiplicative
identity)
Eg
#5)
x2y
Coefficient
=
1
B
Brackets
E
Exponents
D
Division
M
Multiplication
A
Addition
S
Subtraction
**For
a
complex
question
(many
operations)
do
only
1
step
and
rewrite
the
question,
continue
until
solved.
Negative
example:
‐22
=
‐1(22)
=
‐4
(‐2)2
=
(‐2x‐2)
=
+4