Transcript Chapter 8

~ Chapter 8 ~
Exponents & Exponential Functions
Lesson 8-1 Zero & Negative Exponents
Lesson 8-2 Scientific Notation
Lesson 8-3 Multiplication Properties of Exponents
Lesson 8-4 More Multiplication Properties of Exponents
Lesson 8-5 Division Properties of Exponents
Chapter Review
Zero & Negative Exponents
Cumulative Review Chap 1-7
Zero & Negative Exponents
Notes
Zero as an exponent
For every nonzero number a, a
50 = 1
( - 8)0 = 1
0
= 1…
53,4280 = 1
(1/5)0 = 1
Negative Exponents
For every nonzero number a and integer n, a-n = 1/an
10-5 = 1/105
(-6)-9 = 1/(-6)9
x-7 = ?
Simplifying a power
3-4 = 1/34 = 1/81
(-7)0 = 1
(-4)-3 = 1/(-4)3 = 1/(-64)
7-1 = 1/71 = 1/7
An algebraic expression is written in simplest form when it is written with
only positive exponents.
Simplifying an Exponential Expression
4yx-3 = 4y/x3
11m-5 =
7x-4t2 =
2/a-3 =
n-5/v2 =
Zero & Negative Exponents
Notes
Evaluating an Exponential Expression
3m2t-2 for m = 2 and t = -3
3m2/t2 = 3(2)2/(-3)2 =
3(4)/9 = 12/9 = 1 1/3
Evaluate the following for n = -2 & w = 5
n-3w0 =
w0/n3 = 50/(-2)3 =
1/(-8) = - 1/8
n-1/w2 =
1/n1w2 = 1/(-2)1 (5)2
= 1/(-2*25) = - 1/50
1/nw-2 =
w2/n = (5)2/(-2)
= 25/(-2) = -12 1/2
Zero & Negative Exponents
Homework
Homework – Practice 8-1
odd
Scientific Notation
Practice 8-1
Scientific Notation
Practice 8-1
Scientific Notation
Notes
Scientific Notation
Format – has one nonzero digit to the left of the decimal point multiplied by
10 raised to a power. Form: a x 10n, where n is an integer and 1 ≤ a < 10.
Determine if the following numbers are written in scientific notation…
3.42 x 10-7
52 x 104
0.04 x 10-5
Writing a number in scientific notation…
Step 1: Move the decimal until there is one nonzero digit to the left of the
decimal place.
Step 2: Count the number of places the decimal was moved (this is the power
of 10) (If decimal was moved to the left, the power is positive. If the
decimal was moved to the right, the power is negative.)
Step 3: Drop any unneeded zeros.
267,000 =
0.00000000009 =
46,205,000 =
0.0000325=
Scientific Notation
Notes
Writing a Number in Standard Notation
Positive power – move the decimal to right. (value is greater than 1)
Negative power – move the decimal to the left. (value is less than 1)
3.2 x 1012 = 3,200,000,000,000
5.07 x 104 =
5.6 x 10-4 = 0.00056
8.3 x 10-2 =
50,700
0.083
Ordering numbers using Scientific Notation
Step 1: Write each number in scientific notation
Step 2: Order the powers of 10. Arrange the decimals with the same power
of 10 in order.
Step 3: Write the original numbers in order…
Order from least to greatest: 60.2 x 10-5, 63 x 104, 0.067 x 103, and
61 x 10-2
6.02 x 10-4 , 6.1 x 10-1, 6.7 x 101, 6.3 x 105 so…
Scientific Notation
Notes
Multiplying a number in Scientific Notation
2.5(6 x 103) = (2.5 x 6) x 103 = 15 x 103 = 1.5 x 104
0.4(2 x 10-9) =
8(7 x 10-3) =
0.2(3 x 102) =
Scientific Notation
Homework
Homework ~ Practice 8-2 even
Multiplication Properties of Exponents
Practice 8-2
Multiplication Properties of Exponents
Practice 8-2
Multiplication Properties of Exponents
Notes
Multiplying powers with the Same Base
For every nonzero number a and integers m and n, am * an = am + n
53 * 5 6 =
24 * 2-3 =
7-3 * 72 * 76 =
a * a5 =
x * x4 * x3 =
n2 * n3 * 7n =
6y2 * 3y3 *2y-4 =
More multiplying powers in an Algebraic Expression
a * b * a5 =
2y3 * 7x2 * 2y4 =
m2 * n-2 *7m =
Multiplying Numbers in Scientific Notation
(2.5 x 108)(6 x 103) = (2.5 x 6)(108 x 103) = 15 x 1011 = 1.5 x 1012
(1.5 x 10-2)(3 x 104) =
(9 x 10-6)(7 x 10-9) =
Multiplication Properties of Exponents
Homework
Homework – Practice 8-3 odd
More Multiplication Properties of Exponents
Practice 8-3
More Multiplication Properties of
Exponents
Practice 8-3
More Multiplication Properties of Exponents
Notes
Raising a Power to a Power
For every nonzero number a and integers m & n, (am)n = amn
(58)3 =
(n-2)6 =
(xy5)9 =
Remember to simplify…
(a4)7 =
(a-4)7 =
Simplifying an Expression with Powers
(n4)3 * n5 =
t2(t7)-2 =
(a4)2 * (a2)5 =
Raising a Product to a Power
For every nonzero number a and b and integer n, (ab)n = anbn
(5x3)6 =
(8y7)4 =
Simplifying a Product Raised to a power
(6x4y2)-3 =
(4g5)-2 =
(3t0)4 =
More Multiplication Properties of Exponents
Notes
(x-2)2(3xy2)4 = x-2*2(34x4y2*4) = x-4(34x4y8)
=
(c2)3(3c5)4 =
(2a3)5(3ab2)3 =
(6mn)3(5m-3)2 =
Scientific Notation raised to a Power
(2 x 108)4 =
10-3(3 x 105)3 =
34x-4+4y8 = 81x0y8 = 81y8
More Multiplication Properties of
Exponents
Homework
Homework – Practice 8-4
odd
Division Properties of Exponents
Practice 8-4
Division Properties of Exponents
Practice 8-4
Division Properties of Exponents
Notes
Dividing Powers with the Same Base
For every nonzero number a and integers m & n, am = am-n
an
a6 =
a15
c-2d9 =
c9 d 7
x6y-5z4 =
x4y-2z-2
Dividing numbers in Scientific Notation
2 x 103 =
8 x 108
7.5 x 1012 =
2.5 x 10-4
4.2 x 10-7 =
12.6 x 10-2
Raising a Quotient to a Power
For every nonzero number a & b and integer n, (a/b)n = an
bn
(3/x2)2 =
(a/b)-n = a-n =
b-n
(x/y2)4 =
bn
an
(t7/23)2 =
Division Properties of Exponents
Notes
Simplifying an Exponential Expression
(3/4)-3 = (4/3)3 =
(-1/2)-5 = (2/-1)5 =
(2r/s)-1 = (s/2r)1 =
(7a/m)-2 = (m/7a)2 =
Division Properties of Exponents
Homework
Homework ~ Practice 8-5 odd
Division Properties of Exponents
Practice 8-5
Division Properties of Exponents
Practice 8-5
~ Chapter 8 ~
Chapter Review
~ Chapter 8 ~
Chapter 8 Extra Pr
(2) 5/m3 (4) m14/t10
(6) w6j22
(8) 9n8
(10) a4
(14) 2t8
(16) 1/c12
(18) 1/9
(12) 6t4
(20) 144
(26) 6.3 x 10 -4
(24) -64/27
(28) 2 x 10 -4 (30) 6.2 x 109
(32) 8.91 x 10 -10
(38) 63,000
(22) 16
(34) 0.00000032
(40) 5295.6
(36) 0.000425