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LESSON
6.1
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 323–328
GOAL
How to use properties of exponents to evaluate and simplify expressions
involving powers and to use exponents and scientific notation to solve
real-life problems
VOCABULARY
The following are properties of exponents.
Let a and b be real numbers and let m and n be integers.
aman amn
Power of a Power Property
amn amn
Power of a Product Property
abm ambm
Negative Exponent Property
am Zero Exponent Property
a0 1, a 0
Quotient of Powers Property
am
amn, a 0
an
Power of a Quotient Property
b
a
m
Chapter 6
Product of Powers Property
1
,a0
am
am
,b0
bm
A number is expressed in scientific notation if it is in the form c 10 n
where 1 ≤ c < 10 and n is an integer.
EXAMPLE 1
Evaluating Numerical Expressions
a.
36
362
32
34
81
Quotient of powers property
Simplify exponent
Evaluate power.
b. 661 61 1
60
1
Product of powers property
Simplify exponent.
Zero exponent property
Exercises for Example 1
Evaluate the expression.
1. 232
4.
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All rights reserved.
2
3
2. 83
3
5.
8
1
5
3. 324
2
6.
Algebra 2
Practice Workbook with Examples
33
32
103
LESSON
6.1
CONTINUED
EXAMPLE 2
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 323–328
Simplifying Algebraic Expressions
Remember that simplified algebraic expressions contain only positive
exponents.
a.
x7y4
x1y2
b. x7 1y4 2
Quotient of powers property
x8y6
Simplify exponents.
Chapter 6
3x2y4 2
x2 2
32
y4 2
9x4y8
Power of a product property
Power of a power property
8
9y
x4
Negative exponent property
c. 2x5y32 22x52y32
22x10y6
Power of a product property
Power of a power property
1
Negative exponent property
10 6
4x y
Exercises for Example 2
Simplify the expression.
104
7. 2x 25
8.
10. x 2y 43
11.
Algebra 2
Practice Workbook with Examples
y2
y3
9. 33
35
x 4y10
xy3
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All rights reserved.
LESSON
6.1
CONTINUED
EXAMPLE 3
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 323–328
Writing Numbers in Scientific Notation
Alaska is the largest state in the United States, with an area of 1,530,693
square kilometers. Express Alaska’s area in scientific notation.
SOLUTION
1.530693 106
Chapter 6
Recall that a number expressed in scientific notation has the form
c 10 n.
Place the decimal point between the 1 and 5
since 1 ≤ c < 10.
The power of 10 is 6 since the decimal point was shifted
6 places to the left.
The area of Alaska is about 1.5 million square kilometers.
Exercises for Example 3
12. On average, the planet Pluto’s distance from the sun is about 3,670,000,000
miles. Express the distance in scientific notation.
13. The Pacific Ocean is the world’s largest ocean, covering 70,000,000 square
miles of the Earth’s surface. Express this area is scientific notation.
Copyright © McDougal Littell Inc.
All rights reserved.
Algebra 2
Practice Workbook with Examples
105