Download 7 - Spring Branch ISD

7.1 Integer Exponents
7.2 Powers of 10 and Scientific Notation
Algebra I
Name __TEACHER’S NOTES _______
Date ______________
Period ___________
Warm Up:
Evaluate each expression for the given values of the variables.
1. x3 y 2 for x = -1 and y = 10.
2.
3x 2
for x = 4 and y = -7
y2
7.1 Objectives:
 Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.
X is called the “base” . . .
x4
. . . and 4 is called the “exponent.”
What does it mean for an exponent to be negative or 0? Fill in the table and complete the pattern.
When the exponent decreases by one, the value of the power is divided by the base (5). Continue the pattern.
50 =
5
1
5
51 =
1
5
5 2 =
1
1

2
5
25
Example 1: One cup is 2 4 gallons. Simplify this expression.
24 
1
1
1


4
2
(2)(2)(2)(2) 16
Example 2: Simplify
A.
4 3
1
43
B. 7
0
1
C.
1
1

4
(5)
625
(5) 4
1
D. 5
4
1
1

4
5
625
Note
In (–3)–4, the base is negative because the negative sign is inside
the parentheses. In –3–4 the base (3) is positive.
Your Turn 2:
A. 104
B. (2) 4
C. (2) 5
D. 25
Example 3: Evaluate the expression for the given value of the variables. x 2 for x = 4.
(4)-2
=
1
1

2
4
16
Example 4: Evaluate the expression for the given values of the variables.
2a 0b 4 for a = 5 and b = -3.
2(5)0 (3)4  2(1)(
1
1
2
)  (2)( ) 
4
(3)
81 81
Your Turn 4: Evaluate the expression for the given values of the variables.
8a 2b 0 for a = -2 and b = 6.
What if you have an expression with a negative exponent in a denominator, such as
1
?
xn
An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only
positive exponents.
Example 5: Simplify.
A. 7w 4
7w4 
7
w4
B.
5
k 2
C.
a 0b 2
c 3d 6
c3
b2 d 6
5k 2
2
Your Turn 5:
A. 2r 0 m 3
B.
r 3
7
C.
g4
h 6
7.2 Objectives:

Evaluate and _multiply_ by powers of 10.

Convert between standard and scientific notation.
The table shows relationships between several powers of 10.
Each time you divide by 10, the exponent decreases by 1 and the decimal point moves to the left. Each time you multiply by 10,
the exponent increases by 1 and the decimal point moves one place to the right.
POSITIVE INTEGER EXPONENT:
If n is a positive integer, find the value of 10n by starting with 1 and moving the decimal n places to the right:
10 4 = 10,000
NEGATIVE INTEGER EXPONENT:
If n is a negative integer, find the value of 10  n by starting with 1 and moving the decimal n places to the left
104  .0001
Example 1: Find the value of each power of 10.
A. 106
B. 10 4
.000001
C. 109
10,000
1,000,000,000
Your Turn: Find the value of each power of 10.
A. 102
B. 105
C. 1010
Example 2: Write each number as a power of 10.
A. 1,000,000
B. 0.0001
C. 1,000
106
10-4
103
Your Turn: Write each number as a power of 10.
A. 100,000,000
B. 0.0001
C. 0.1
3
Scientific notation is a method of writing numbers that are very small or large. A number written in scientific notation has two
parts that are multiplied. One is the base – which must be a number greater than or equal to 1, and less than 10; and the other is a
power of 10:
Example: Saturn has a diameter of about 1.2  105 km. Its distance from the Sun is about 1,427,000,000 km.
A. Write Saturn’s diameter in standard form.
120,000
B. Write Saturn’s distance from the Sun in scientific notation.
1.427 x 109
Your Turn: Use the information to write Jupiter’s diameter in scientific notation. 143,000 km
Your Turn: Use the information to write Jupiter’s orbital speed in standard form. 1.3  10 4 m/s.
Example 5: Order the list of numbers from least to greatest.
5.4 x 10-3, 1 X 10-2, 1.3 x 10-2, 6.3 x 103, 2.1 x 106, 4.1 X 106
Your Turn: Order the list of numbers from least to greatest.
1.5 x 10-2, 3.2 x 10-4, 1.1 x 102, 5.2 x 103,
4
7.0 x 102, 5.3 x 103