Download Chapter Six –Linear Equations and Their Graphs

Chapter Eight –Zero and Negative Exponents (8-1)
WORD BANK:
base
power
Scientific notation
standard notation
properties of exponents
geometric sequence
growth factor
common ratio
exponential function
You can use____________ to show repeated multiplication with the same integer.
Example: “102” means 10 * 10 or 100. “10” is the_________. “2” is the_____________.
Together they are read “10 to the second__________.”
Any number raised to the zero power is equal to 1.
Example: 30 = 1
20 = 1
100 = 1
Have a negative exponent? Change your altitude!
Example: 3-2 = 1 OR 1
10-2 = 1 OR 1__
2
3
9
102
100
The following problems are copied from Prentice Hall Algebra I:
Practice: (p. 397) Simplify each expression:
#5) (- 4) -2
#9) 1
20
#7) 2 -6
#11) (- 4) -3
#18) 5x- 4
#19) 1
x -7
#20) 1
c -1
#21) 5 – 2
p
#27)
#32) 7s0t-5
2-1m2
8
2c -3
Evaluate each expression for s = 5
#33) s-2
#36) s0
#37) 3s-2
#38) (2s)-2
Answers: 5) 1/16; 7) 1/64; 9) 1; 11) – 1/64; 18) 5/x4 ; 19) x7; 20) c; 21) 1/25p; 27) 4c3; 32)14/m2t5; 33) 1/25; 36) 1; 37) 3/25; 38)
1
/100
Chapter Eight –Scientific Notation (8-2)
___________ ___________ allows us to write very large and very small numbers with
ease by using powers of ten.
Example: 7,500,000,000,000 = 7.5 * 1012
.0000000000075 = 7.5 * 10-12
The first factor is always written as an integer greater than 1 but less than 10. The
exponent is the number of digits that come after (or in the case of negative exponents:
before) the decimal point in the original number. In the example above the exponent is
12 because there are twelve digits after the 7.
To multiply with scientific notation, add the exponents.
To divide with scientific notation, subtract the exponents.
____________ _____________ is the product of the two factors, or the original number.
In the example above, 7,500,000,000,000 is the number in standard notation.
Practice: (p 403) Write each number in scientific notation:
#7) 9,040,000,000
#9) 9.3 million
#13) 0.00092
Write each number in standard notation:
#18) 7.2 x 105
#19) 8.97 x 10-1
#20) 1.3 x 100
#21) 2.74 x 10-5
Order from least to greatest:
#25) 50.1 x 10-3, 4.8 x 10-1, 0.52 x 10-3, 56 x 10 -2
Simplify each expression using scientific notation:
#28) 8(7 x 10-3)
#30) 0.2(3 x 102)
#29) 8(3 x 1014)
Answers: 7) 9.04 x 109; 9) 9.3 x 106; 13) 9.2 x 10-4; 18) 720,000; 19) 0.897; 20) 1.3; 21) 0.0000274; 25) 0.52 x 10-3, 50.1 x
10-3, 4.8 x 10-1, 56 x 10-2; 28) 5.6 x 10-2; 29) 2.4 x 1015; 30) 6.0 x 101
Chapter Eight –Properties of Exponents (8-3) (8-4) (8-5)
To multiply numbers with the same base, add the exponents.
Example: 23 * 24 = 23+4 = 27
To raise a power to a power, multiply the exponents.
Example: (23)4 = 23*4 = 212
To simplify a product raised to a power, multiply the each factor by the exponent.
Example: (ab)4 = a4 b4
Practice: (p 413-15) Simplify each expression:
#5) (c5)3c4
#6) (d3)5 (d3)0
#7) (t2)- 2 (t2)- 5
#8) (x3)- 1 (x2)5
#11) (7a)2
#13) (6y2)2
#19) (mg4)-1 (mg4)
#21) (3b- 2)2(a2b4)3
#23) ( 4 x 105)2
#30) (3.5 x 10- 4)3
#25) (2 x 10- 10)3
Solve: #63) 82 = 2x
#57) Write each as a power of 10:
a) How many cubic centimeters are in a cubic meter?
b) How many cubic millimeters are in a cubic meter?
c) How many cubic meters are in a cubic kilometer?
d) How many cubic millimeters are in a cubic kilometer?
Answers: 5) c 19; 6) d 15; 7) 1/ t 14: 8) x 7; 11) 49a2; 18) 8x5 y 3; 19) 1; 21) 9a6 b8; 23) 1.6 x 1011; 24) 9 x 1010;
30) 4.2875 x10 - 11; 63) 6; 57) a) 106; b) 109; c) 109; d) 1018
Chapter Eight –Properties of Exponents (8-3) (8-4) (8-5)
To raise a quotient to a power, raise both the numerator and the denominator to the
power.
Example: ( 2/3 )4
= 24 / 34
OR: 16 / 81
To divide powers with the same base, subtract the exponent in the denominator from
the exponent in the numerator.
Example: x4 / x3
=
x 4–3
OR: x1 OR: x
Practice: (pp420+21) Simplify each expression:
#5) 25 / 27
#6) 27 / 25
#8) m - 2 / m – 5
#11) c2 d - 3 / c3 d – 1
#13) 6.5 x 1015
1.3 x 108
#14) 2.7 x 10 - 8
9 x 10 - 4
#19) In 2000, people in the U.S. over age 2 watched T.V. a total of 386 billion hours. The
population of the U.S. over age 2 was about 265 million people.
a) Write each number in scientific notation.
b) What was the average number of hours per person?
c) How many hours a day did each person watch on average?
#26)
(3 / 3 )
#29)
#31)
(- / )
#32) - 2/3
#34)
(
3
2
4n/
4
3
2
–2
)
2n2
3
(/)
2
3
-1
( )
–3
(
)
#35) c5 / c9
3
Answers: 5) ¼; 6) 2; 8) m3; 11) 1/ cd2; 13) 5 x 107; 14) 3 x 10 – 5; 19a) 3.86 x 1011 hours, and 2.65 x 108 people; b) about
1457 hours; c) about 4 hours a day; 26) 1/9; 29) 3/2; 31) 9/4; 32) – 27/ 8; 34) 8/ n3; 35) 1/c12
Chapter Eight –Geometric Sequences and Exponential Functions
(8-6)
You form a geometric sequence by multiplying a term in the sequence by a fixed
number. This fixed number is called the common ratio.
A (n ) = a * r n – 1
where n = the term number,
a = the first number in the sequence,
and r = the common ratio.
Example:
3, 12, 48, … has a common ratio of 4, because you multiply each term by 4 to find the
next term.
So substituting we get: A (n) = 3 * 4 n – 1 as our rule for this sequence.
Practice: (p.427) Find the common ratio then write a rule for each:
#3) 70, 7, 0.7, 0.07,…
#6) 0.45, 0.9, 1.8, 3.6, …
#13) 2, 14, 98, 686, …
#32) 0.1, 0.9, 8.1, 72.9, …
An exponential function is a function in the form y = a * b x, where a is a nonzero
constant, b is greater than 0 and not equal to 1, and x is a real number.
Examples: y = o.5 * 2x
f (x) = -2 * 0.5x
Practice: (p. 428+29)
#36) Fold a paper in half, making 2 rectangles. If you fold it in half again, you divide the
paper into 4 rectangles. Suppose you were to keep doing this.
a) Complete the table below:
# of Folds
# of Rectangles
0
1
1
2
2
4
3
4
5
b) Write a rule to represent this pattern.
c) Suppose you could continue to fold the paper. How many rectangles would there
be if you could fold it 10 times?
Answers: 3) 0.1 is the common ratio, A(n)= 70* (0.1)n -1; 6) 2 is the common ratio, A(n) = 0.45 * (2) n-1; 13) 7 is the common
ratio, A(n) = 2 *(7)n – 1; 32) 9 is the common ratio, A(n) = 0.1 *(9)n – 1; 36a) 3=8, 4=16, 5=32; b) A(n) = 2 * 2n-1OR A(n)=1*2n;
c) 1024 rectangles.