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1 x 3 y 2 z 1 . This fraction can be written without negative exponents by moving all the f a c t o r s from the denominator to the numerator . Change the sign of each exponent: 3 to + 3 , 2 to + 2 , 1 to + 1. 1 x 3 y 2 z 1 = x 3 y 2 z 1 = x 3 y 2 z

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Practice set b

Write each of the following so that only positive exponents appear.

x 3 y 4 z 8

x 3 y 4 z 8

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6 m 3 n 2 7 k 1

6 k 7 m 3 n 2

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1 a 2 b 6 c 8

a 2 b 6 c 8

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3 a ( a 5 b ) 2 5 b ( a 4 b ) 5

3 a 5 b ( a 5 b ) 2 ( a 4 b ) 5

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Sample set c

Rewrite 24 a 7 b 9 2 3 a 4 b 6 in a simpler form.

Notice that we are dividing powers with the same base. We’ll proceed by using the rules of exponents.

24 a 7 b 9 2 3 a 4 b 6 = 24 a 7 b 9 8 a 4 b 6 = 3 a 7 4 b 9 ( 6 ) = 3 a 3 b 9 + 6 = 3 a 3 b 15

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Write 9 a 5 b 3 5 x 3 y 2 so that no denominator appears.

We can eliminate the denominator by moving all factors that make up the denominator to the numerator.

9 a 5 b 3 5 1 x 3 y 2

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Find the value of 1 10 2 + 3 4 3 .

We can evaluate this expression by eliminating the negative exponents.

1 10 2 + 3 4 3 = 1 10 2 + 3 4 3 = 1 100 + 3 64 = 100 + 192 = 292

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Practice set c

Rewrite 36 x 8 b 3 3 2 x 2 b 5 in a simpler form.

4 x 10 b 8

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Write 2 4 m 3 n 7 4 1 x 5 in a simpler form and one in which no denominator appears.

64 m 3 n 7 x 5

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Find the value of 2 5 2 + 6 2 2 3 3 2 .

52

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Exercises

Write the following expressions using only positive exponents. Assume all variables are nonzero.

( x 5 ) 3

1 ( x 5 ) 3

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( a + 9 ) 10

1 ( a + 9 ) 10

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( a 1 ) 12

1 ( a 1 ) 12

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x 3 y 2 z 6

x 3 y 2 z 6

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a 7 b 9 z w 3

a 7 z w 3 b 9

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x 5 y 5 z 2

x 5 y 5 z 2

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x 4 y 8 z 3 w 4

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a 4 b 6 c 1 d 4

d 4 a 4 b 6 c

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x 9 y 6 z 1 w 5 r 2

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7 a 2 b 2 c 2

7 b 2 c 2 a 2

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4 x 3 ( x + 1 ) 2 y 4 z 1

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7 a 2 ( a 4 ) 3 b 6 c 7

7 a 2 ( a 4 ) 3 b 6 c 7

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18 b 6 ( b 2 3 ) 5 c 4 d 5 e 1

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7 ( w + 2 ) 2 ( w + 1 ) 3

7 ( w + 1 ) 3 ( w + 2 ) 2

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2 ( a 8 ) 3 ( a 2 ) 5

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( x 2 + 3 ) 3 ( x 2 1 ) 4

( x 2 + 3 ) 3 ( x 2 1 ) 4

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( x 4 + 2 x 1 ) 6 ( x + 5 ) 4

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( 3 x 2 4 x 8 ) 9 ( 2 x + 11 ) 3

1 ( 3 x 2 4 x 8 ) 9 ( 2 x + 11 ) 3

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( 5 y 2 + 8 y 6 ) 2 ( 6 y 1 ) 7

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7 a ( a 2 4 ) 2 ( b 2 1 ) 2

7 a ( a 2 4 ) 2 ( b 2 1 ) 2

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( x 5 ) 4 3 b 2 c 4 ( x + 6 ) 8

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( y 3 + 1 ) 1 5 y 3 z 4 w 2 ( y 3 1 ) 2

5 y 3 ( y 3 + 1 ) z 4 w 2 ( y 3 1 ) 2

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3 y 3 ( 9 x )

27 x y 3

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4 a 2 b 2 a 5 b 2

4 a 3

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5 1 a 2 b 6 b 11 c 3 c 9

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2 3 x 2 2 3 x 2

1

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7 a 3 b 9 5 a b 6 c 2 c 4

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( x + 5 ) 2 ( x + 5 ) 6

1 ( x + 5 ) 4

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( a 4 ) 3 ( a 4 ) 10

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8 ( b + 2 ) 8 ( b + 2 ) 4 ( b + 2 ) 3

8 ( b + 2 ) 9

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3 a 5 b 7 ( a 2 + 4 ) 3 6 a 4 b ( a 2 + 4 ) 1 ( a 2 + 4 )

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4 a 3 b 5 ( 2 a 2 b 7 c 2 )

8 a 5 b 2 c 2

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2 x 2 y 4 z 4 ( 6 x 3 y 3 z )

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( 5 ) 2 ( 5 ) 1

5

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( 1 ) 1 ( 1 ) 1

1

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3 c 5 a 3 b 3

3 b 3 c 5 a 3

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16 a 2 b 6 c 2 y z 5 w 4

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24 y 2 z 8 6 a 2 b 1 c 9 d 3

4 b c 9 y 2 a 2 d 3 z 8

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3 1 b 5 ( b + 7 ) 4 9 1 a 4 ( a + 7 ) 2

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36 a 6 b 5 c 8 3 2 a 3 b 7 c 9

4 a 3 b 2 c

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45 a 4 b 2 c 6 15 a 2 b 7 c 8

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3 3 x 4 y 3 z 3 2 x y 5 z 5

3 x 3 y 2 z 4

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21 x 2 y 2 z 5 w 4 7 x y z 12 w 14

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33 a 4 b 7 11 a 3 b 2

3 a 7 b 5

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51 x 5 y 3 3 x y

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2 6 x 5 y 2 a 7 b 5 2 1 x 4 y 2 b 6

128 a 7 b x

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( x + 3 ) 3 ( y 6 ) 4 ( x + 3 ) 5 ( y 6 ) 8

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23 a 4 b 5 c 2 x 6 y 5

23 a 4 b 5 x 6 c 2 y 5

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2 3 b 5 c 2 d 9 4 b 4 c x

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10 x 3 y 7 3 x 5 z 2

10 3 x 2 y 7 z 2

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3 x 2 y 2 ( x 5 ) 9 1 ( x + 5 ) 3

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14 a 2 b 2 c 12 ( a 2 + 21 ) 4 4 2 a 2 b 1 ( a + 6 ) 3

224 b 3 c 12 ( a 2 + 21 ) 4 ( a + 6 ) 3

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For the following problems, evaluate each numerical expression.

2 1 3 1 4 1

1 24

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10 2 + 3 ( 10 2 )

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2 1 + 4 1 2 2 + 4 2

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21 0 2 6 2 6 13

63

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For the following problems, write each expression so that only positive exponents appear.

( m 0 ) 1 , m 0

1

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( x 6 y 6 z 1 ) 2

x 12 y 12 z 2

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( a 5 b 1 c 0 ) 6

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( y 3 x 4 ) 5

x 20 y 15

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( 2 a b 3 ) 4

16 a 4 b 12

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( 5 1 a 3 b 6 x 2 y 9 ) 2

a 6 x 4 25 b 12 y 18

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( 4 m 3 n 6 2 m 5 n ) 3

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( r 5 s 4 m 8 n 7 ) 4

n 28 s 16 m 32 r 20

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( h 2 j 6 k 4 p ) 5

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Exercises for review

( [link] ) Simplify ( 4 x 5 y 3 z 0 ) 3

64 x 15 y 9

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( [link] ) Find the sum. 15 + 3 .

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( [link] ) Find the difference. 8 ( 12 ) .

20

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( [link] ) Simplify ( 3 ) ( 8 ) + 4 ( 5 ) .

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( [link] ) Find the value of m if m = 3 k 5 t k t + 6 when k = 4 and t = 2 .

1

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
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what is inorganic
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Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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answer
Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Who can show me the full solution in this problem?
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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