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Use the Definition of a Negative Exponent

In the following exercises, simplify.


3 −4
10 −2

1 81 1 100

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2 −8
10 −2

1 256 1 100

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1 c −5
1 3 −2

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1 c −5
1 5 −2

c 5 25

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1 q −10
1 10 −3

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1 t −9
1 10 −4

t 9 10000

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( 5 8 ) −2
( 3 m n ) −2

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( 3 10 ) −2
( 2 c d ) −3

100 9 c 3 d 3 8

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( 4 9 ) −3
( u 2 2 v ) −5

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( 7 2 ) −3
( 3 x y 2 ) −3

8 343 x 3 y 6 27

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( 5 ) 2
5 −2
( 1 5 ) −2
( 1 5 ) −2

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( −7 ) −2
7 2
( 1 7 ) −2
( 1 7 ) −2

1 49 1 49 49 −49

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3 −3
( 1 3 ) −3
( 1 3 ) −3
( −3 ) −3

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5 −3
( 1 5 ) −3
( 1 5 ) −3
( −5 ) −3

1 125 −125 −125 1 125

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3 · 5 −1
( 3 · 5 ) −1

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2 · 5 −1
( 2 · 5 ) −1

2 5 1 10

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4 · 5 −2
( 4 · 5 ) −2

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3 · 4 −2
( 3 · 4 ) −2

3 16 1 144

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m −4
( x 3 ) −4

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b −5
( k 2 ) −5

1 b 5 1 k 10

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p −10
( q 6 ) −8

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s −8
( a 9 ) −10

1 s 8 1 a 90

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7 n −1
( 7 n ) −1
( −7 n ) −1

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6 r −1
( 6 r ) −1
( −6 r ) −1

6 r 1 6 r 1 6 r

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( 3 p ) −2
3 p −2
−3 p −2

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( 2 q ) −4
2 q −4
−2 q −4

1 16 q 4 2 q 4 2 q 4

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Simplify Expressions with Integer Exponents

In the following exercises, simplify.


b 4 b −8
r −2 r 5
x −7 x −3

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s 3 · s −7
q −8 · q 3
y −2 · y −5

1 s 4 1 q 5 1 y 7

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a 3 · a −3
a · a 3
a · a −3

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y 5 · y −5
y · y 5
y · y −5

1 y 6 1 y 4

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x 4 · x −2 · x −3

1 x

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( w 4 x −5 ) ( w −2 x −4 )

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( m 3 n −3 ) ( m −5 n −1 )

1 m 2 n 4

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( u v −2 ) ( u −5 v −3 )

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( p q −4 ) ( p −6 q −3 )

1 p 5 q 7

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( −6 c −3 d 9 ) ( 2 c 4 d −5 )

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( −2 j −5 k 8 ) ( 7 j 2 k −3 )

14 k 5 j 3

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( −4 r −2 s −8 ) ( 9 r 4 s 3 )

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( −5 m 4 n 6 ) ( 8 m −5 n −3 )

40 n 3 m

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Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

0.00000103

1.03 × 10 −6

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Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

1.6 × 10 10

16,000,000,000

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1.93 × 10 −5

0.0000193

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Multiply and Divide Using Scientific Notation

In the following exercises, multiply. Write your answer in decimal form.

( 3 × 10 −5 ) ( 3 × 10 9 )

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( 2 × 10 2 ) ( 1 × 10 −4 )

0.02

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( 7.1 × 10 −2 ) ( 2.4 × 10 −4 )

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( 3.5 × 10 −4 ) ( 1.6 × 10 −2 )

5.6 × 10 −6

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In the following exercises, divide. Write your answer in decimal form.

7 × 10 −3 1 × 10 −7

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5 × 10 −2 1 × 10 −10

500,000,000

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8 × 10 6 4 × 10 −1

20,000,000

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Everyday math

The population of the United States on July 4, 2010 was almost 310,000,000. Write the number in scientific notation.

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The population of the world on July 4, 2010 was more than 6,850,000,000. Write the number in scientific notation

6.85 × 10 9 .

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The average width of a human hair is 0.0018 centimeters. Write the number in scientific notation.

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The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.

5.7 × 10 −10

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In 2010, the number of Facebook users each day who changed their status to ‘engaged’ was 2 × 10 4 . Convert this number to decimal form.

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At the start of 2012, the US federal budget had a deficit of more than $ 1.5 × 10 13 . Convert this number to decimal form.

15,000,000,000,000

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The concentration of carbon dioxide in the atmosphere is 3.9 × 10 −4 . Convert this number to decimal form.

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The width of a proton is 1 × 10 −5 of the width of an atom. Convert this number to decimal form.

0.00001

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Health care costs The Centers for Medicare and Medicaid projects that consumers will spend more than $4 trillion on health care by 2017.

  1. Write 4 trillion in decimal notation.
  2. Write 4 trillion in scientific notation.
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Practice Key Terms 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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