Name: Class: Algebra 2C Homework Exponent RulesName Date...

Name:_________________________________________ Class:_________________________________________ Hour:_________________________________________

Algebra 2C Homework Exponent Rules Integer Exponents

Copyright © by Holt, Rinehart and Winston. 5 Holt Algebra 1All rights reserved.

Name Date Class

LESSON Practice CInteger Exponents7-1

Simplify.

1. 4 !2 1 ___ 16

2. 6 0 1 3. ! 6 !2

! 1 ___ 36

4. ! !1 " !5 !1 5. ! !3 " !2 1 __ 9

6. 5 !3

1 ____ 125

7. ! 7 !3 ! 1 ____

343

8. ! !4 " !5 ! 1 _____

1024

9. ! !9 " 0 1

Evaluate each expression for the given value(s) of the variable(s).

10. x !4 y 3 for x " 2 and y " 3 11. 5r !3 s !6 for r " 3 and s " 1

27 ___ 16

5 ___ 27

12. ! 3 ! m " !4 for m " 6 13. ! 2a !1 b !3 for a " 2 and b " 3

1 ___ 81

! 1 ___ 27

14. ! !2xy " !3 for x " !2 and y " 1 __ 2 15. ! 4 __

5 m " !3

for m " 10

1 __ 8

1 ____ 512

Simplify.

16. x !3 1 ___ x 3

17. z 0 1 18. t !9 1 __ t 9

19. 3n !2 3 ___ n 2

20. 2 __ 3

x !4 2 ____ 3 x 4

21. !a !2 ! 1 ___ a 2

22. 10r !3 s 4 10 s 4 _____ r 3

23. b 3 ______ c !2 d 3

b 3 c 2 _____ d 3

24. 5x !2 y !3

________ z 0

5 _____ x 2 y 3

25. p !9 q !4

_______ r 2 s !3

s 3 ________ p 9 q 4 r 2

26. a 0 b !2 ______

c !3 d c 3 _____

b 2 d 27.

g 3 h !2 _______

k !1 j !5

g 3 kj 5 ______ h 2

28. A micrometer is an instrument that can measure the thickness of an object very accurately. One micrometer is accurate to within 1 0 !4 inches. Evaluate this expression.

1 ______ 10,000

inch or 0.0001 inch

29. An object is being measured by a micrometer. It has athickness of 6 !3 inches. Evaluate this expression.

1 ____ 216

inch or 0.00463 inch

a107c07-1_pr.indd 5a107c07-1_pr.indd 5 6/23/06 4:40:07 PM6/23/06 4:40:07 PMProcess BlackProcess Black


Name Date Class


Simplify.

1. 4 !2 1 ___ 16

2. 6 0 1 3. ! 6 !2

! 1 ___ 36

4. ! !1 " !5 !1 5. ! !3 " !2 1 __ 9

6. 5 !3

1 ____ 125

7. ! 7 !3 ! 1 ____

343

8. ! !4 " !5 ! 1 _____

1024

9. ! !9 " 0 1



27 ___ 16

5 ___ 27


1 ___ 81

! 1 ___ 27

14. ! !2xy " !3 for x " !2 and y " 1 __ 2 15. ! 4 __

5 m " !3

for m " 10

1 __ 8

1 ____ 512

Simplify.

16. x !3 1 ___ x 3

17. z 0 1 18. t !9 1 __ t 9

19. 3n !2 3 ___ n 2

20. 2 __ 3

x !4 2 ____ 3 x 4

21. !a !2 ! 1 ___ a 2

22. 10r !3 s 4 10 s 4 _____ r 3

23. b 3 ______ c !2 d 3

b 3 c 2 _____ d 3

24. 5x !2 y !3

________ z 0

5 _____ x 2 y 3

25. p !9 q !4

_______ r 2 s !3

s 3 ________ p 9 q 4 r 2

26. a 0 b !2 ______

c !3 d c 3 _____

b 2 d 27.

g 3 h !2 _______

k !1 j !5

g 3 kj 5 ______ h 2


1 ______ 10,000

inch or 0.0001 inch


1 ____ 216




Name Date Class


Simplify.

1. 4 !2 1 ___ 16

2. 6 0 1 3. ! 6 !2

! 1 ___ 36

4. ! !1 " !5 !1 5. ! !3 " !2 1 __ 9

6. 5 !3

1 ____ 125

7. ! 7 !3 ! 1 ____

343

8. ! !4 " !5 ! 1 _____

1024

9. ! !9 " 0 1



27 ___ 16

5 ___ 27


1 ___ 81

! 1 ___ 27

14. ! !2xy " !3 for x " !2 and y " 1 __ 2 15. ! 4 __

5 m " !3

for m " 10

1 __ 8

1 ____ 512

Simplify.

16. x !3 1 ___ x 3

17. z 0 1 18. t !9 1 __ t 9

19. 3n !2 3 ___ n 2

20. 2 __ 3

x !4 2 ____ 3 x 4

21. !a !2 ! 1 ___ a 2

22. 10r !3 s 4 10 s 4 _____ r 3

23. b 3 ______ c !2 d 3

b 3 c 2 _____ d 3

24. 5x !2 y !3

________ z 0

5 _____ x 2 y 3

25. p !9 q !4

_______ r 2 s !3

s 3 ________ p 9 q 4 r 2

26. a 0 b !2 ______

c !3 d c 3 _____

b 2 d 27.

g 3 h !2 _______

k !1 j !5

g 3 kj 5 ______ h 2


1 ______ 10,000

inch or 0.0001 inch


1 ____ 216




Name Date Class

LESSON

7-1Practice BInteger Exponents

Simplify.

1. 5 !3 " 1 _______

5 3

" 1 _____ 125

2. 2 !6 " 1 _______

2 6

" 1 _____ 64

3. ! !5 " !2 1 ___ 25

4. ! ! 4 " !3 ! 1 ___ 64

5. ! 6 0 !1 6. ! 7 " !2 1 ___ 49


7. d !3 for d " !2 8. a 5 b !6 for a " 3 and b " 2 9. ! b ! 4 " !2 for b " 1

! 1 __

8

243 ____ 64

1 __ 9

10. 5z –x for z " !3 and x " 2 11. ! 5z " !x for z " !3 and x " 2 12. c !3 ! 16 !2 " for c " 4

5 __ 9 1 ____

225 1 ______

16,384

Simplify.

13. t !4 14. 3r !5 15. s !3 ____ t !5

1 __ t 4

3 __ r 5

t 5 ___

s 3

16. h 0 ___ 3

17. 2x !3 y !2

________ z 4

18. 4fg !5

_____ 5h !3

1 __ 3 2 _______

x 3 y 2 z 4 4fh 3 ____

5g 5

19. 14a !4 _______ 20bc !1

20. a 4 c 2 e 0 _______ b !1 d !3

21. ! 3g !2 hk !2

__________ ! 6h 0

7c ______ 10 a 4 b

a 4 bc 2 d 3 h ______ 2 g 2 k 2

22. A cooking website claims to contain 1 0 5 recipes.Evaluate this expression. 100,000

23. A ball bearing has diameter 2 !3 inches.Evaluate this expression. 1 __

8 inch or 0.125 inch

a107c07-1_pr.indd 4a107c07-1_pr.indd 4 12/26/05 7:45:03 AM12/26/05 7:45:03 AMProcess BlackProcess Black


Name Date Class

LESSON

7-1Practice BInteger Exponents

Simplify.

1. 5 !3 " 1 _______

5 3

" 1 _____ 125

2. 2 !6 " 1 _______

2 6

" 1 _____ 64

3. ! !5 " !2 1 ___ 25

4. ! ! 4 " !3 ! 1 ___ 64

5. ! 6 0 !1 6. ! 7 " !2 1 ___ 49


7. d !3 for d " !2 8. a 5 b !6 for a " 3 and b " 2 9. ! b ! 4 " !2 for b " 1

! 1 __

8

243 ____ 64

1 __ 9

10. 5z –x for z " !3 and x " 2 11. ! 5z " !x for z " !3 and x " 2 12. c !3 ! 16 !2 " for c " 4

5 __ 9 1 ____

225 1 ______

16,384

Simplify.

13. t !4 14. 3r !5 15. s !3 ____ t !5

1 __ t 4

3 __ r 5

t 5 ___

s 3

16. h 0 ___ 3

17. 2x !3 y !2

________ z 4

18. 4fg !5

_____ 5h !3

1 __ 3 2 _______

x 3 y 2 z 4 4fh 3 ____

5g 5

19. 14a !4 _______ 20bc !1

20. a 4 c 2 e 0 _______ b !1 d !3

21. ! 3g !2 hk !2

__________ ! 6h 0

7c ______ 10 a 4 b

a 4 bc 2 d 3 h ______ 2 g 2 k 2

22. A cooking website claims to contain 1 0 5 recipes.Evaluate this expression. 100,000

23. A ball bearing has diameter 2 !3 inches.Evaluate this expression. 1 __

8 inch or 0.125 inch



Name Date Class


Simplify.

1. 4 !2 1 ___ 16

2. 6 0 1 3. ! 6 !2

! 1 ___ 36

4. ! !1 " !5 !1 5. ! !3 " !2 1 __ 9

6. 5 !3 1 ____ 125

7. ! 7 !3 ! 1 ____

343

8. ! !4 " !5 ! 1 _____

1024

9. ! !9 " 0 1



27 ___ 16

5 ___ 27


1 ___ 81

! 1 ___ 27

14. ! !2xy " !3 for x " !2 and y " 1 __ 2

15. ! 4 __ 5

m " !3 for m " 10

1 __ 8 1 ____

512

Simplify.

16. x !3 1 ___ x 3

17. z 0 1 18. t !9 1 __ t 9

19. 3n !2 3 ___ n 2

20. 2 __ 3

x !4 2 ____ 3 x 4

21. !a !2 ! 1 ___ a 2

22. 10r !3 s 4 10 s 4 _____ r 3

23. b 3 ______ c !2 d 3

b 3 c 2 _____ d 3

24. 5x !2 y !3

________ z 0

5 _____ x 2 y 3

25. p !9 q !4

_______ r 2 s !3

s 3 ________ p 9 q 4 r 2

26. a 0 b !2 ______

c !3 d c 3 _____

b 2 d 27.

g 3 h !2 _______

k !1 j !5

g 3 kj 5 ______ h 2


1 ______ 10,000

inch or 0.0001 inch


1 ____ 216




Name Date Class


Simplify.

1. 4 !2 1 ___ 16

2. 6 0 1 3. ! 6 !2

! 1 ___ 36

4. ! !1 " !5 !1 5. ! !3 " !2 1 __ 9

6. 5 !3 1 ____ 125

7. ! 7 !3 ! 1 ____

343

8. ! !4 " !5 ! 1 _____

1024

9. ! !9 " 0 1



27 ___ 16

5 ___ 27


1 ___ 81

! 1 ___ 27

14. ! !2xy " !3 for x " !2 and y " 1 __ 2

15. ! 4 __ 5

m " !3 for m " 10

1 __ 8 1 ____

512

Simplify.

16. x !3 1 ___ x 3

17. z 0 1 18. t !9 1 __ t 9

19. 3n !2 3 ___ n 2

20. 2 __ 3

x !4 2 ____ 3 x 4

21. !a !2 ! 1 ___ a 2

22. 10r !3 s 4 10 s 4 _____ r 3

23. b 3 ______ c !2 d 3

b 3 c 2 _____ d 3

24. 5x !2 y !3

________ z 0

5 _____ x 2 y 3

25. p !9 q !4

_______ r 2 s !3

s 3 ________ p 9 q 4 r 2

26. a 0 b !2 ______

c !3 d c 3 _____

b 2 d 27.

g 3 h !2 _______

k !1 j !5

g 3 kj 5 ______ h 2


1 ______ 10,000

inch or 0.0001 inch


1 ____ 216



Name:_________________________________________ Class:_________________________________________ Hour:_________________________________________

Multiplication Properties of Exponents


Name Date Class


Simplify.

1. 4 !2 1 ___ 16

2. 6 0 1 3. ! 6 !2

! 1 ___ 36

4. ! !1 " !5 !1 5. ! !3 " !2 1 __ 9

6. 5 !3 1 ____ 125

7. ! 7 !3 ! 1 ____

343

8. ! !4 " !5 ! 1 _____

1024

9. ! !9 " 0 1



27 ___ 16

5 ___ 27


1 ___ 81

! 1 ___ 27

14. ! !2xy " !3 for x " !2 and y " 1 __ 2

15. ! 4 __ 5

m " !3 for m " 10

1 __ 8 1 ____

512

Simplify.

16. x !3 1 ___ x 3

17. z 0 1 18. t !9 1 __ t 9

19. 3n !2 3 ___ n 2

20. 2 __ 3

x !4 2 ____ 3 x 4

21. !a !2 ! 1 ___ a 2

22. 10r !3 s 4 10 s 4 _____ r 3

23. b 3 ______ c !2 d 3

b 3 c 2 _____ d 3

24. 5x !2 y !3

________ z 0

5 _____ x 2 y 3

25. p !9 q !4

_______ r 2 s !3

s 3 ________ p 9 q 4 r 2

26. a 0 b !2 ______

c !3 d c 3 _____

b 2 d 27.

g 3 h !2 _______

k !1 j !5

g 3 kj 5 ______ h 2


1 ______ 10,000

inch or 0.0001 inch


1 ____ 216




Name Date Class

LESSON Practice CMultiplication Properties of Exponents7-3

Simplify.

1. 2 3 · 2 5 2. 6 4 · 6 1 3. 5 6 · 5 !2

2 8 or 256 6 5 or 7776 5 4 or 625 4. t !4 · t !5 5. x 4 · x 2 6. s 4 · s 6 · t 3

t !9 x 6 s 10 t 3 7. ! 2 4 " 2 8. ! m 4 " 0 9. ! y !2 " !4

2 8 or 256 1 y 8 10. m 4 · ! n 2 " 3 · n !2 11. y · x 3 · ! y 2 " 2 · ! x 3 " 6 12. ! 4x " 3

m 4 n 4 x 21 y 5 64 x 3 13. ! gh " !1 14. ! ! 3bc " 2 15. ! j 2 k 3 " 3

1 ___ gh

!9 b 2 c 2 j 6 k 9

16. ! 5d " 2 · d 4 17. ! 3x y 3 " !2 · ! 9y " 2 18. ! r !3 s 4 " 2 · ! r 2 s 7 " 0

25 d 6 9 _____ x 2 y 4

s 8 ___ r 6

19. ! a 2 b !2 " !3 · ! a !1 b 2 " !3 20. ! x 3 y !1 " 4 · ! x !2 y 2 " !3 21. ! ! j !3 k !2 " 2 · ! j 2 " 6

1 ___ a 3

x 18 ___ y 10

! j 6

___ k 4

Find the missing exponent in each expression.

22. b 4

· b 5 " b 9 23. ! t 3 "

4

" t 12 24. ! h 3 " !2

" 1 ___ h 6

25. Most states are irregularly shaped. However, the shapesof some western states approximate rectangles.Wyoming is nearly rectangular, with a width of about1.5 # 1 0 6 feet and a length of about 1.9 # 1 0 6 feet. What is the approximate area of Wyoming? Write your answer in scientific notation. 2.85 " 1 0 12 square feet



Name Date Class

LESSON

7-3Practice BMultiplication Properties of Exponents

Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2

22. The pitch of a sound is determined by the number ofvibrations produced per second. The note “middle C”produces 2.62 " 1 0 2 vibrations per second. If a pianistplays middle C for 5 " 1 0 !1 seconds, how many vibrationswill occur?

1.31 " 1 0 2 or 131 vibrations



Name Date Class


Simplify.

1. 2 3 · 2 5 2. 6 4 · 6 1 3. 5 6 · 5 !2

2 8 or 256 6 5 or 7776 5 4 or 625 4. t !4 · t !5 5. x 4 · x 2 6. s 4 · s 6 · t 3

t !9 x 6 s 10 t 3 7. ! 2 4 " 2 8. ! m 4 " 0 9. ! y !2 " !4

2 8 or 256 1 y 8 10. m 4 · ! n 2 " 3 · n !2 11. y · x 3 · ! y 2 " 2 · ! x 3 " 6 12. ! 4x " 3

m 4 n 4 x 21 y 5 64 x 3 13. ! gh " !1 14. ! ! 3bc " 2 15. ! j 2 k 3 " 3

1 ___ gh

!9 b 2 c 2 j 6 k 9

16. ! 5d " 2 · d 4 17. ! 3x y 3 " !2 · ! 9y " 2 18. ! r !3 s 4 " 2 · ! r 2 s 7 " 0

25 d 6 9 _____ x 2 y 4

s 8 ___ r 6

19. ! a 2 b !2 " !3 · ! a !1 b 2 " !3 20. ! x 3 y !1 " 4 · ! x !2 y 2 " !3 21. ! ! j !3 k !2 " 2 · ! j 2 " 6

1 ___ a 3

x 18 ___ y 10

! j 6

___ k 4


22. b 4

· b 5 " b 9 23. ! t 3 "

4

" t 12 24. ! h 3 " !2

" 1 ___ h 6




Name Date Class

LESSON


Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2





Name Date Class

LESSON


Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2





Name Date Class

LESSON


Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2





Name Date Class

LESSON


Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2





Name Date Class

LESSON


Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2





Name Date Class

LESSON


Simplify.

1. 3 4 · 3 2 2. 2 5 · 2 4 3. 2 3 · 2 5 · 2 1

3 6 or 729 2 9 or 512 2 9 or 512 4. q !6 · q !1 5. r !3 · r 4 · s !4 6. j !2 · j !4 · j 2

1 ___ q 7

r ___ s 4

1 __ j 4

7. c 5 · b !2 · c 3 8. ! h 2 " 5 9. ! g 4 " !2

c 8 ___ b 2

h 10

1 ___ g 8

10. ! w 6 " 0 11. ( v 2 ) 5 · v 4 12. ( w 5 ) !2 · w !3

1 v 14 1 ____ w 13

13. ! f 6 " !4 · ! f !2 " !3 14. ! a !2 " !3 · ! a 5 " 2 15. ! 3b " 4

1 ___ f 18

a 16 81 b 4

16. ! !5k " 2 17. ! ! 4m " 3 18. ! !3p " !2

25 k 2

!64 m 3

1 ____ 9 p 2

19. ! s 4 t " 3 · ! s 4 t 3 " 2 20. ! a 2 b 4 " 2 · ! a !2 b 3 " !1 · a 4 21. ! x 3 y 2 " !4 · ! x 2 y !3 " !2

s 20 t 9

a 10 b 5

1 ______ x 16 y 2





Name Date Class


Simplify.

1. 2 3 · 2 5 2. 6 4 · 6 1 3. 5 6 · 5 !2

2 8 or 256 6 5 or 7776 5 4 or 625 4. t !4 · t !5 5. x 4 · x 2 6. s 4 · s 6 · t 3

t !9 x 6 s 10 t 3 7. ! 2 4 " 2 8. ! m 4 " 0 9. ! y !2 " !4

2 8 or 256 1 y 8 10. m 4 · ! n 2 " 3 · n !2 11. y · x 3 · ! y 2 " 2 · ! x 3 " 6 12. ! 4x " 3

m 4 n 4 x 21 y 5 64 x 3 13. ! gh " !1 14. ! ! 3bc " 2 15. ! j 2 k 3 " 3

1 ___ gh

!9 b 2 c 2 j 6 k 9

16. ! 5d " 2 · d 4 17. ! 3x y 3 " !2 · ! 9y " 2 18. ! r !3 s 4 " 2 · ! r 2 s 7 " 0

25 d 6 9 _____ x 2 y 4

s 8 ___ r 6

19. ! a 2 b !2 " !3 · ! a !1 b 2 " !3 20. ! x 3 y !1 " 4 · ! x !2 y 2 " !3 21. ! ! j !3 k !2 " 2 · ! j 2 " 6

1 ___ a 3

x 18 ___ y 10

! j 6

___ k 4


22. b 4

· b 5 " b 9 23. ! t 3 "

4

" t 12 24. ! h 3 " !2

" 1 ___ h 6



Name:_________________________________________ Class:_________________________________________ Hour:_________________________________________

Division Properties of Exponents


Name Date Class

LESSON

7-4Practice BDivision Properties of Exponents

Simplify.

1. 6 7 ___ 6 5

! 6 7 " 5 ! 6 2 ! 36 2. t

12 ___ t 7

! t 12 " 7

! t 5

3. w 9 ___ w 2

4. j 2

__ j 8

5. 20 m 5 _____ 4 m 2

w 7

1 __ j 6

5 m 3

6. c 3 d 2 _____ c 2 d 5

7. ! x 4 " 2 _____ ! x 3 " 5

8. ! s 3 t ___ st 4

" 2

c ___ d 3

1 ___ x 7

s 4 ___ t 6

9. ! 2 __ 3

" "3 10. ! 3a ___

2b " "4

11. " ! "t ___ 3v

" "4

27 ___ 8 16 b 4 _____

81 a 4 ! 81 v 4 _____

t 4

12. ! 6 __ 7

" "2 · ! 4s ___

6t " "2

13. ! 3c ___ "2

" "1 ! d __

4 " "2

14. ! ! 3mn ____ 2

" "1 " "4

49 t 2 _____ 16 s 2

! 32 _____ 3c d 2

81 m 4 n 4 ________ 16

Simplify. Write the answer in scientific notation.

15. ! 3.8 # 1 0 5 " $ ! 1.9 # 1 0 "6 " 16. ! 2.5 # 1 0 3 " $ ! 5 # 1 0 "4 "

2 " 1 0 11 5 " 1 0 6 17. A textile factory produces 1.08 # 1 0 8 yards of fabric every

year. If the factory is in operation 360 days a year, what isthe average number of yards of fabric produced each day?Give your answer in standard form.

300,000 yards 18. It takes 5 yards of fabric to manufacture a dress. If the textile

factory turned their entire yearly production of 1.08 # 10 8 yardsof fabric into dresses, how many could they make? Give your answer in scientific notation.

2.16 " 10 7 dresses



Name Date Class

LESSON


Simplify.

1. 6 7 ___ 6 5

! 6 7 " 5 ! 6 2 ! 36 2. t

12 ___ t 7

! t 12 " 7

! t 5

3. w 9 ___ w 2

4. j 2

__ j 8

5. 20 m 5 _____ 4 m 2

w 7

1 __ j 6

5 m 3

6. c 3 d 2 _____ c 2 d 5

7. ! x 4 " 2 _____ ! x 3 " 5

8. ! s 3 t ___ st 4

" 2

c ___ d 3

1 ___ x 7

s 4 ___ t 6

9. ! 2 __ 3

" "3 10. ! 3a ___

2b " "4

11. " ! "t ___ 3v

" "4

27 ___ 8 16 b 4 _____

81 a 4 ! 81 v 4 _____

t 4

12. ! 6 __ 7

" "2 · ! 4s ___

6t " "2

13. ! 3c ___ "2

" "1 ! d __

4 " "2

14. ! ! 3mn ____ 2

" "1 " "4

49 t 2 _____ 16 s 2

! 32 _____ 3c d 2

81 m 4 n 4 ________ 16


15. ! 3.8 # 1 0 5 " $ ! 1.9 # 1 0 "6 " 16. ! 2.5 # 1 0 3 " $ ! 5 # 1 0 "4 "





2.16 " 10 7 dresses



Name Date Class

LESSON


Simplify.

1. 6 7 ___ 6 5

! 6 7 " 5 ! 6 2 ! 36 2. t

12 ___ t 7

! t 12 " 7

! t 5

3. w 9 ___ w 2

4. j 2

__ j 8

5. 20 m 5 _____ 4 m 2

w 7

1 __ j 6

5 m 3

6. c 3 d 2 _____ c 2 d 5

7. ! x 4 " 2 _____ ! x 3 " 5

8. ! s 3 t ___ st 4

" 2

c ___ d 3

1 ___ x 7

s 4 ___ t 6

9. ! 2 __ 3 " "3

10. ! 3a ___ 2b

" "4 11. " ! "t ___

3v " "4

27 ___ 8 16 b 4 _____

81 a 4 ! 81 v 4 _____

t 4

12. ! 6 __ 7 " "2

· ! 4s ___ 6t

" "2 13. ! 3c ___

"2 " "1

! d __ 4 " "2

14. ! ! 3mn ____ 2 " "1

" "4

49 t 2 _____ 16 s 2

! 32 _____ 3c d 2

81 m 4 n 4 ________ 16


15. ! 3.8 # 1 0 5 " $ ! 1.9 # 1 0 "6 " 16. ! 2.5 # 1 0 3 " $ ! 5 # 1 0 "4 "





2.16 " 10 7 dresses



Name Date Class

LESSON


Simplify.

1. 6 7 ___ 6 5

! 6 7 " 5 ! 6 2 ! 36 2. t

12 ___ t 7

! t 12 " 7

! t 5

3. w 9 ___ w 2

4. j 2

__ j 8

5. 20 m 5 _____ 4 m 2

w 7

1 __ j 6

5 m 3

6. c 3 d 2 _____ c 2 d 5

7. ! x 4 " 2 _____ ! x 3 " 5

8. ! s 3 t ___ st 4

" 2

c ___ d 3

1 ___ x 7

s 4 ___ t 6

9. ! 2 __ 3

" "3 10. ! 3a ___

2b " "4

11. " ! "t ___ 3v

" "4

27 ___ 8

16 b 4 _____ 81 a 4

! 81 v 4 _____ t 4

12. ! 6 __ 7

" "2 · ! 4s ___

6t " "2

13. ! 3c ___ "2

" "1 ! d __

4 " "2

14. ! ! 3mn ____ 2

" "1 " "4

49 t 2 _____ 16 s 2

! 32 _____ 3c d 2

81 m 4 n 4 ________ 16


15. ! 3.8 # 1 0 5 " $ ! 1.9 # 1 0 "6 " 16. ! 2.5 # 1 0 3 " $ ! 5 # 1 0 "4 "





2.16 " 10 7 dresses



Name Date Class

LESSON Practice CDivision Properties of Exponents7-4

Simplify.

1. 6 8 ___ 6 6

2. h 4 ____ h !3

3. 2 3 · 4 3 · 5 ________ 5 2 · 2 4

6 2 or 36 h 7 32 ___ 5

4. x 5 y 2

_____ xy 3

5. m 3 n 6 ________ m 4 n 4 p 8

6. a 5 b 2 c 3 _______ a 6 b 2 c

x 4 ___ y n 2 _____ mp 8

c 2 ___ a

7. ! 4 __ 7

" !2 8. ! s 2 __

t 3 " 2 " 9. ! ! ab ___

6c " 5

49 ___ 16

s 4 ___ t 6

! a 5 b 5 _______ 7776 c 5

10. ! ! b 2 c _____ 2 d 3 f 4

" !2

11. ! xy z 2 ____ !w " 5 " 12. ! 1 0 3 · 1 0 2 ________

1 0 !6 " !4

! 4 d 6 f 8 ______ b 4 c 2

! x 5 y 5 z 10

________ w 5

1 ____ 1 0 44


13. ! 6.4 # 1 0 7 " $ ! 1.6 # 1 0 3 " 14. ! 8.1 # 1 0 !6 " $ ! 9 # 1 0 !15 "

4 " 1 0 4 9 " 1 0 8 15. ! 2.8 # 1 0 2 " $ ! 7 # 1 0 !9 " 16. ! 4.8 # 1 0 5 " $ ! 6 # 1 0 13 "

4 " 1 0 10 8 " 1 0 !9

Find the missing exponent in each equation.

17. ! c 4

___ d

" !2

" d 2 ___ c 8

18. b 14 ____

b 7

" b 7 19. ! s !3 ____

t 4 " !3

" s 9 t 12

20. An actor was paid $2.1 # 1 0 6 to star in a movie. If themovie was 1 hr 45 min long, what was the actor’s salaryper minute? Give your answer standard form. $20,000 per minute



Name Date Class


Simplify.

1. 6 8 ___ 6 6

2. h 4 ____ h !3

3. 2 3 · 4 3 · 5 ________ 5 2 · 2 4

6 2 or 36 h 7 32 ___ 5

4. x 5 y 2

_____ xy 3

5. m 3 n 6 ________ m 4 n 4 p 8

6. a 5 b 2 c 3 _______ a 6 b 2 c

x 4 ___ y n 2 _____ mp 8

c 2 ___ a

7. ! 4 __ 7

" !2 8. ! s 2 __

t 3 " 2 " 9. ! ! ab ___

6c " 5

49 ___ 16

s 4 ___ t 6

! a 5 b 5 _______ 7776 c 5

10. ! ! b 2 c _____ 2 d 3 f 4

" !2

11. ! xy z 2 ____ !w " 5 " 12. ! 1 0 3 · 1 0 2 ________

1 0 !6 " !4

! 4 d 6 f 8 ______ b 4 c 2

! x 5 y 5 z 10

________ w 5

1 ____ 1 0 44


13. ! 6.4 # 1 0 7 " $ ! 1.6 # 1 0 3 " 14. ! 8.1 # 1 0 !6 " $ ! 9 # 1 0 !15 "

4 " 1 0 4 9 " 1 0 8 15. ! 2.8 # 1 0 2 " $ ! 7 # 1 0 !9 " 16. ! 4.8 # 1 0 5 " $ ! 6 # 1 0 13 "

4 " 1 0 10 8 " 1 0 !9


17. ! c 4

___ d

" !2

" d 2 ___ c 8

18. b 14 ____

b 7

" b 7 19. ! s !3 ____

t 4 " !3

" s 9 t 12




Name Date Class


Simplify.

1. 6 8 ___ 6 6

2. h 4 ____ h !3

3. 2 3 · 4 3 · 5 ________ 5 2 · 2 4

6 2 or 36 h 7 32 ___ 5

4. x 5 y 2

_____ xy 3

5. m 3 n 6 ________ m 4 n 4 p 8

6. a 5 b 2 c 3 _______ a 6 b 2 c

x 4 ___ y n 2 _____ mp 8

c 2 ___ a

7. ! 4 __ 7

" !2 8. ! s 2 __

t 3 " 2 " 9. ! ! ab ___

6c " 5

49 ___ 16

s 4 ___ t 6

! a 5 b 5 _______ 7776 c 5

10. ! ! b 2 c _____ 2 d 3 f 4

" !2

11. ! xy z 2 ____ !w " 5 " 12. ! 1 0 3 · 1 0 2 ________

1 0 !6 " !4

! 4 d 6 f 8 ______ b 4 c 2

! x 5 y 5 z 10

________ w 5

1 ____ 1 0 44


13. ! 6.4 # 1 0 7 " $ ! 1.6 # 1 0 3 " 14. ! 8.1 # 1 0 !6 " $ ! 9 # 1 0 !15 "

4 " 1 0 4 9 " 1 0 8 15. ! 2.8 # 1 0 2 " $ ! 7 # 1 0 !9 " 16. ! 4.8 # 1 0 5 " $ ! 6 # 1 0 13 "

4 " 1 0 10 8 " 1 0 !9


17. ! c 4

___ d

" !2

" d 2 ___ c 8

18. b 14 ____

b 7

" b 7 19. ! s !3 ____

t 4 " !3

" s 9 t 12




Name Date Class


Simplify.

1. 6 8 ___ 6 6

2. h 4 ____ h !3

3. 2 3 · 4 3 · 5 ________ 5 2 · 2 4

6 2 or 36 h 7 32 ___ 5

4. x 5 y 2

_____ xy 3

5. m 3 n 6 ________ m 4 n 4 p 8

6. a 5 b 2 c 3 _______ a 6 b 2 c

x 4 ___ y n 2 _____ mp 8

c 2 ___ a

7. ! 4 __ 7

" !2 8. ! s 2 __

t 3 " 2 " 9. ! ! ab ___

6c " 5

49 ___ 16

s 4 ___ t 6

! a 5 b 5 _______ 7776 c 5

10. ! ! b 2 c _____ 2 d 3 f 4

" !2

11. ! xy z 2 ____ !w " 5 " 12. ! 1 0 3 · 1 0 2 ________

1 0 !6 " !4

! 4 d 6 f 8 ______ b 4 c 2

! x 5 y 5 z 10

________ w 5

1 ____ 1 0 44


13. ! 6.4 # 1 0 7 " $ ! 1.6 # 1 0 3 " 14. ! 8.1 # 1 0 !6 " $ ! 9 # 1 0 !15 "

4 " 1 0 4 9 " 1 0 8 15. ! 2.8 # 1 0 2 " $ ! 7 # 1 0 !9 " 16. ! 4.8 # 1 0 5 " $ ! 6 # 1 0 13 "

4 " 1 0 10 8 " 1 0 !9


17. ! c 4

___ d

" !2

" d 2 ___ c 8

18. b 14 ____

b 7

" b 7 19. ! s !3 ____

t 4 " !3

" s 9 t 12



Name:_________________________________________ Class:_________________________________________ Hour:_________________________________________

Rational Exponents

614 Chapter 8 Rational and Radical Functions

GUIDED PRACTICE 1. Vocabulary The index of the expression

3 ! " 4 2 is ### ? . (2, 3, or 4)

SEE EXAMPLE 1 p. 610

Find all real roots.

2. cube roots of 27 3. fourth roots of 625 4. cube roots of 0


Simplify each expression. Assume that all variables are positive.

5. 3 ! "" 8 x 3 6. 4 $ "" 32 _

x 4 7. 3 $

""" 125 x 6 _

6 8. ! "" 50 x 3

9. 4 ! " x 8 ·

3 ! " x 4 10. 3 $

"" x 5 _

4 11.

! "" 40 x 4 _ 3 ! "" - x 3

12. 4 $ """

x 12 y 4

_ 3


Write each expression in radical form, and simplify.

13. 36 3 _ 2

14. 32

3 _ 5

15. (-27)

1 _ 3

16. 8

2 _ 3


Write each expression by using rational exponents.

17. 5 ! "" 9 10 18. ! " 8 3 19. ( 6 ! " 5 )

3 20. ( 3 ! " 27 )

2


Simplify each expression.

21. 13 1 _ 2

· 13

3 _ 2

22. 9

4 _ 3

_

9 2 _ 3

23. ( 64 1 _ 2

)

1 _ 3

24. ( 8 _ 27

) 1 _ 3

25. 25 - 1 _

2 26. 7

1 _ 4

· 7

- 3 _ 4

27. (-125)

- 1 _ 3

28. ( 6

1 _ 2

)

6


29. Geometry The side length of a cube can be determined by finding the cube root of the volume. What is the side length to the nearest inch of the cube shown?

KEYWORD: MB7 Parent

KEYWORD: MB7 8-6

8-6

THINK AND DISCUSS 1. Explain why n ! " a n is equal to a for all natural numbers a and n.

2. GET ORGANIZED Copy and complete the graphic organizer. In each box, give a numeric and an algebraic example of the given property of rational exponents.

ExercisesExercises

a207se_c08l06_0610_0617.indd 614a207se_c08l06_0610_0617.indd 614 12/16/05 6:07:25 PM12/16/05 6:07:25 PM

8- 6 Radical Expressions and Rational Exponents 615

Suppose that a cheetah, a lion, a house cat, and the fastest human runner competed in a 100 m race. At top speed, the cheetah would finish in 3.20 s, the lion in 4.47 s, the house cat in 7.46 s, and the human in 9.77 s.

Biology

Typical Body Mass

Animal Mass (kg)

House cat 4.5

Cheetah 55.0

Lion 170.0

PRACTICE AND PROBLEM SOLVING

For See Exercises Example

30–32 1 33–40 2 41–44 3 45–48 4 49–56 5 57 6

Independent Practice Find all real roots.

30. cube roots of -64 31. fifth roots of 32 32. fourth roots of -16


33. 3 ! " 9x · 3 ! "" 3 x 2 34.

4 ! """ 324 x 8 35. 3 #

"" x 6 _

250 36. !

"" x 5 _

45

37. 3 ! "" 56 x 9 38.

4 ! "" x 10 _ 4 ! " x 4

39. 5 ! " x 7 ·

5 ! " x 6 40. 3 ! """" -54 x 9 y 3


41. 64 1 _ 2

42. 216

2 _ 3

43. (-1000)

4 _ 3

44. 6

3 _ 2


45. 3 ! "" 14 3 46. ( 5 ! "" -8 )

4 47. ( 4 ! "" 144 )

2 48. ! "" 48 3


49. (8 · 64) 2 _ 3

50. 144

- 1 _ 2

51. ( 2 3 _

27 )

1 _ 3

52. 2

1 _ 2

· 2

1 _ 4

53. ( 49 _ 81

) - 1 _

2 54. 12

1 _ 4

_

12 3 _ 4

55. ( 5 1 _ 3

)

1 _ 3

56. ( 27 _

27 1 _ 3

) 1 _ 2

57. Banking The initial amount deposited in a savings account is $1000. The amount a in dollars in the account after t years can be represented by the function

a (t) = 1000 ( 2 t _ 24

) . To the nearest dollar, what will the amount in the account be after

6 years?

58. Biology The formula P = 73.3 4 ! "" m 3 , known as

Kleiber’s law, relates the metabolism rate P of an organism in Calories per day and the body mass m of the organism in kilograms. The table shows the typical body mass of several members of the cat family.

a. What is the metabolism rate of a cheetah to the nearest Calorie per day?

b. Multi-Step Approximately how many more Calories of food does a lion need to consume each day than a house cat does?

59. Medicine Iodine-131 is a radioactive material used to treat certain types of cancer. Iodine-131 has a half-life of 8 days, which means that it takes 8 days for half of an initial sample to decay. The percent of radioactive material that remains after t days

can be determined from the expression 100 ( 1 __ 2 ) t _ h

, where h is the half-life in days.

a. What percent of a sample of iodine-131 will remain after 20 days? b. What if...? Another form of radioactive iodine used in cancer treatment

is iodine-125. Iodine-125 has a half-life of 59 days. A hospital has 20 g of iodine-125 and 20 g of iodine-131 left over from treating patients. How much more iodine-125 than iodine-131 will remain after a period of 30 days?

60. Meteorology The formula W = 35.74 + 0.6215T - 35.75 V 4 _ 25

+ 0.4275T V

4 _ 25

relates

the wind chill temperature W to the air temperature T in degrees Fahrenheit and the wind speed V in miles per hour. Use a calculator to find the wind chill to the nearest degree when the air temperature is 40°F and the wind speed is 35 mi/h.

Skills Practice p. S19Application Practice p. S39

Extra Practice


614 Chapter 8 Rational and Radical Functions

GUIDED PRACTICE 1. Vocabulary The index of the expression

3 ! " 4 2 is ### ? . (2, 3, or 4)


Find all real roots.

2. cube roots of 27 3. fourth roots of 625 4. cube roots of 0



5. 3 ! "" 8 x 3 6. 4 $ "" 32 _

x 4 7. 3 $

""" 125 x 6 _

6 8. ! "" 50 x 3

9. 4 ! " x 8 ·

3 ! " x 4 10. 3 $

"" x 5 _

4 11.

! "" 40 x 4 _ 3 ! "" - x 3

12. 4 $ """

x 12 y 4

_ 3



13. 36 3 _ 2

14. 32

3 _ 5

15. (-27)

1 _ 3

16. 8

2 _ 3



17. 5 ! "" 9 10 18. ! " 8 3 19. ( 6 ! " 5 )

3 20. ( 3 ! " 27 )

2



21. 13 1 _ 2

· 13

3 _ 2

22. 9

4 _ 3

_

9 2 _ 3

23. ( 64 1 _ 2

)

1 _ 3

24. ( 8 _ 27

) 1 _ 3

25. 25 - 1 _

2 26. 7

1 _ 4

· 7

- 3 _ 4

27. (-125)

- 1 _ 3

28. ( 6

1 _ 2

)

6


29. Geometry The side length of a cube can be determined by finding the cube root of the volume. What is the side length to the nearest inch of the cube shown?

KEYWORD: MB7 Parent

KEYWORD: MB7 8-6

8-6

THINK AND DISCUSS 1. Explain why n ! " a n is equal to a for all natural numbers a and n.

2. GET ORGANIZED Copy and complete the graphic organizer. In each box, give a numeric and an algebraic example of the given property of rational exponents.

ExercisesExercises


8- 6 Radical Expressions and Rational Exponents 615

Suppose that a cheetah, a lion, a house cat, and the fastest human runner competed in a 100 m race. At top speed, the cheetah would finish in 3.20 s, the lion in 4.47 s, the house cat in 7.46 s, and the human in 9.77 s.

Biology

Typical Body Mass

Animal Mass (kg)

House cat 4.5

Cheetah 55.0

Lion 170.0

PRACTICE AND PROBLEM SOLVING

For See Exercises Example

30–32 1 33–40 2 41–44 3 45–48 4 49–56 5 57 6

Independent Practice Find all real roots.

30. cube roots of -64 31. fifth roots of 32 32. fourth roots of -16


33. 3 ! " 9x · 3 ! "" 3 x 2 34.

4 ! """ 324 x 8 35. 3 #

"" x 6 _

250 36. !

"" x 5 _

45

37. 3 ! "" 56 x 9 38.

4 ! "" x 10 _ 4 ! " x 4

39. 5 ! " x 7 ·

5 ! " x 6 40. 3 ! """" -54 x 9 y 3


41. 64 1 _ 2

42. 216

2 _ 3

43. (-1000)

4 _ 3

44. 6

3 _ 2


45. 3 ! "" 14 3 46. ( 5 ! "" -8 )

4 47. ( 4 ! "" 144 )

2 48. ! "" 48 3


49. (8 · 64) 2 _ 3

50. 144

- 1 _ 2

51. ( 2 3 _

27 )

1 _ 3

52. 2

1 _ 2

· 2

1 _ 4

53. ( 49 _ 81

) - 1 _

2 54. 12

1 _ 4

_

12 3 _ 4

55. ( 5 1 _ 3

)

1 _ 3

56. ( 27 _

27 1 _ 3

) 1 _ 2

57. Banking The initial amount deposited in a savings account is $1000. The amount a in dollars in the account after t years can be represented by the function

a (t) = 1000 ( 2 t _ 24

) . To the nearest dollar, what will the amount in the account be after

6 years?

58. Biology The formula P = 73.3 4 ! "" m 3 , known as

Kleiber’s law, relates the metabolism rate P of an organism in Calories per day and the body mass m of the organism in kilograms. The table shows the typical body mass of several members of the cat family.

a. What is the metabolism rate of a cheetah to the nearest Calorie per day?

b. Multi-Step Approximately how many more Calories of food does a lion need to consume each day than a house cat does?

59. Medicine Iodine-131 is a radioactive material used to treat certain types of cancer. Iodine-131 has a half-life of 8 days, which means that it takes 8 days for half of an initial sample to decay. The percent of radioactive material that remains after t days

can be determined from the expression 100 ( 1 __ 2 ) t _ h

, where h is the half-life in days.

a. What percent of a sample of iodine-131 will remain after 20 days? b. What if...? Another form of radioactive iodine used in cancer treatment

is iodine-125. Iodine-125 has a half-life of 59 days. A hospital has 20 g of iodine-125 and 20 g of iodine-131 left over from treating patients. How much more iodine-125 than iodine-131 will remain after a period of 30 days?

60. Meteorology The formula W = 35.74 + 0.6215T - 35.75 V 4 _ 25

+ 0.4275T V

4 _ 25

relates

the wind chill temperature W to the air temperature T in degrees Fahrenheit and the wind speed V in miles per hour. Use a calculator to find the wind chill to the nearest degree when the air temperature is 40°F and the wind speed is 35 mi/h.

Skills Practice p. S19Application Practice p. S39

Extra Practice


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