#### Transcript Document

```Algebra 1
Section 1.7
Definition
For x  N, bx is the product of
x factors of b.
The
repeated
factor,
b,
is
the
When numbers are written this
base.
way, they are said to be in
The exponent
[x] indicates
exponential
form or
how many
times bnotation.
is used as a
exponential
factor.
Exponents
63 = 6 × 6 × 6
“6 to the third power”
“6 cubed”
6
6
6
Exponents
52 = 5 × 5
“5 to the second power”
“5 squared”
5
5
Example 1
a. 2 • 2 • 2 • 2 • 2 • 2 • 2 = 27
b. -3 • (-3) • (-3) • (-3) = (-3)4
An Important Distinction
-34 = -1 • 34 = -81
(-3)4 = -3 • (-3) • (-3) • (-3) = 81
Example 2
Evaluate:
a. 93 = 9 • 9 • 9 = 729
b. (-7)4 = -7 • (-7) • (-7) • (-7) =
2401
c. -42 = -(4 • 4) = -16
Properties of Exponents
52 • 53
52+3
85 ÷ 82
8•8•8•8•8
8•8
55
85-2
(5 • 5)(5 • 5 • 5)
83
Properties of Exponents
Product Property: To multiply
xa • xb = xa+b
Properties of Exponents
Quotient Property: To divide
like bases, subtract the
exponents.
xa
a-b for x  0
=
x
xb
Properties of Exponents
Power Property: To raise a
power to a power, multiply the
exponents.
(xa)b = xab
Example 3
Leave in exponential form:
a. 52 • 510 = 52+10 = 512
b. 32 • 34 • 39 = 32+4+9 = 315
c. 24 ÷ 2 = 24-1 = 23
d. 105 ÷ 103 = 105-3 = 102
e. (53)6 = 53(6) = 518
Properties of Exponents
The Quotient Property allows
us to give meaning to negative
exponents.
x2
2-3 = x-1
=
x
x3
x2
1
=
x3
x1
Properties of Exponents
Any nonzero number to the
zero power equals 1.
When x  0, x0 = 1
Properties of Exponents
Negative exponents:
x-a
1
= a
x
1
a
=
x
x-a
Example 4
Evaluate.
1
1
=
a. (-2)-4 =
(-2)4
16
1
1
b. -3-2 = - 2 = 9
3
1
c. -3 = 63 = 216
6
Example 5
in positive exponential form:
1
a. 3-9 • 37 = 3-9+7 = 3-2 = 2
3
1
b. 2-3 • 2-2 = 2-3+(-2) = 2-5 = 5
2
Example 5