Section 1.8 Properties of Integer Exponents Scientific Notation

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```					           Section 1.8

Properties of Integer Exponents
& Scientific Notation

(81)
Objectives
(81)

Be able
to use the properties of exponents
to simplify expressions with
exponents
to utilize scientific notation
8.1.8 Properties of Exponents
(81)

Property                             Example
xm • xn = xm+n                      x3 • x4 = x3+4 = x7
xm / xn = xm-n                      x7 / x2 = x7-2 = x5
x-n = 1 / xn; 1 / x-n = xn            x-5 / y-4 = y4 / x5
(x • y)n = xn • yn                   (x • y)3 = x3 • y3
(x / y)n = xn / yn                    (x / y)3 = x3 / y3
x0 = 1 (x ≠ 0)                                   30 = 1
Skill Practice
(82)

1.   (-3)2 = (-3) • (-3) = 9
2.   - 32 = - (3) • (3) = -9
3.   -3-2 = -[(3)-1]2 = -[1/3]2 = -[12/32] = -1/9
4.   ( -8y)0 = 1 (assuming y ≠ 0)
5.   -60 = -(6)0 = -1
Example
96 a2 b-3 c-4 d5 e6     (break constant into product of primes)

72 a3 b2 c-3 d5 e-2     (flip/flop negative exponents)

25 3 a2 1 c3 d5 e6e2
23 32 a3 b2b3 c4 d5 1
22 1 1     1    1 1           e8
1 3 a     b5     c 1          1
22 e8   or    4 e8      .

3 a b5        3 a b5
Skill Practice
(84)

6.       (a5b-3)4 = (a5/b3)4 = a5•4/b3•4 = a20/b12
7.       (2/3)-1 + 4-1 – (1/4)0 = 3/2 + 1/4 - 1
= 6/4 + 1/4 - 4/4 = 3/4
8.
.
( 2 b-3 c-2 )3 =   (   1 b2 1 )3 =   ( 1 1 1 )3 = 1   .

4 b-2 c              2 b3 c c2       2 b c3    23b3c9
9.       (x3y-4)2 (x-2y)-4 = (x6y-8)(x8y-4)
= (x6/y8)(x8/y4)
= (x6+8/y8+4) = x14/y12
Scientific Notation
(84)

Used extensively prior to hand held computers.
Values are written as ±x.xxxxx × 10n
Note: one nonzero digit left of decimal, n is an ± integer
Examples: -7.348765 × 102   -734.8765                        →2
5.45455 × 103     5454.55                         →3
-2.735 × 10-4     -0.0002735                       ←4
6.4708 × 10-3     .0064708                        ←3
4.7867824 × 1043 (normal use)
Solve using Scientific Notation
(2.342×103) (-6.234×106) = (2.342)(-6.234)×103106
= -14.600028×109
4.7876 × 10-5   =  4.7876 × 10-5
6.4535 × 107        6.4535 107
= 0.741861 × 10-5-7
= 0.741861 × 10-12
= 7.41861 × 10-13      (subtract 1)
Homework 1.8

Pg 87      17, 25, 35
Pg 88      37, 63, 67, 73
Pg 89      97, 101
Objectives
(81)

Be able
to use the properties of exponents
to simplify expressions with
exponents
to identify scientific notations
Section 1.8

Properties of Integer Exponents
& Scientific Notation

(81)

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