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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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Questions & Answers

how many typos can we find...?
Chris Reply
5
Joseph
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!
Chris Reply
4x+7y=29,x+3y=11 substitute method of linear equation
Srinu Reply
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
I want to learn
Elizebeth
help
Elizebeth
I want to learn. Please teach me?
Wayne
1) Use any equation, and solve for any of the variables. Since the coefficient of x (the number in front of the x) in the second equation is 1 (it actually isn't shown, but 1 * x = x), use that equation. Subtract 3y from both sides (this isolates the x on the left side of the equal sign).
bruce
2) This results in x=11-3y. x is note in terms of y. Use that as the value of x and substitute for all x in the first equation. The first equation becomes 4(11-3y)+7y =29. Note that the only variable left in the first equation is the y. If you have multiple variable, then something is wrong.
bruce
3) Distribute (multiply) the 4 across 11-3y to get 44-12y. Add this to the 7y. So, the equation is now 44-5y=29.
bruce
4) Solve 44-5y=29 for y. Isolate the y by subtracting 44 from birth sides, resulting in -5y=-15. Now, divide birth sides by -5 (since you have -5y). This results in y=3. You now have the value of one variable.
bruce
5) The last step is to take the value of y from Step 4) and substitute into the 2nd equation. Therefore: x+3y=11 becomes x+3(3)=11. Then multiplying, x+9=11. Finally, solve for x by subtracting 9 from both sides. Therefore, x=2.
bruce
6) The ordered pair of (2, 3) is the proposed solution. To check, substitute those values into either equation. If the result is true, then the solution is correct. 4(2)+7(3)=8+21=29. TRUE! Finished.
bruce
At 1:30 Marlon left his house to go to the beach, a distance of 5.625 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 1.5 times his walking speed. Find his speed when skateboarding and when walking.
Andrew Reply
divide 3x⁴-4x³-3x-1 by x-3
Ritik Reply
how to multiply the monomial
Ceny Reply
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Juned Reply
Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
ashley Reply
app is wrong how can 350 be divisible by 3.
Raheem Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna Reply
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Lorris Reply
I'm getting "math processing error" on math problems. Anyone know why?
Ray Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
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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