8-5:DIVISIONPROPERTIESOFEXPONENTS

LessonObjectives:• Dividepowerswiththesamebase• Raiseaquotienttoapower

PROPERTY:DIVIDINGPOWERSWITHTHESAMEBASEForeverynonzeronumberaandintegersmandn,a) 3

7

34 b) x

2

x5

EXAMPLE1:SIMPLIFYINGAPOWERRAISEDTOAPOWERSimplifyeachexpression.1. a

6

a14 2. n

−8

n4 3. c

15

c9 4. 7

−3

7−5

5. m

6

m10 6. 46

48 7. 4

−1

42 8. z

7

z−3

9. c

−1d3

c5d−4 10. x

7y9z3

x4y7z8 11. a

6b−5

a−2b7

12. a

7b5

a6b 13. m

8n3

m10n5 14. x

4y−8z−2

x−1y6z−10

II x

3 5

aanme.am

c's sass

I He 7,6A a

Z

47 Is

xz

a

Hy xf

EXAMPLE2:DIVIDINGNUMBERSINSCIENTIFICNOTATIONSimplifyeachquotient.Writeeachanswerinscientificnotation.15. 8×10

9

4×105 16. 9.5×10

9

5×104 17. 6.4×10

9

8×107 18.1.8×10

−8

0.9×103

PROPERTY:RAISINGAQUOTIENTTOAPOWERForeverynonzeronumbersaandbandintegern,a) 4

5⎛

⎝⎜⎞

⎠⎟3

EXAMPLE3:RAISINGAQUOTIENTTOAPOWERSimplifyeachexpression.

19. a2

b3⎛

⎝⎜

⎞

⎠⎟

5

20. 5a0b4

c−3⎛

⎝⎜

⎞

⎠⎟

2

21. a8b6

a11⎛

⎝⎜

⎞

⎠⎟

5

22. a2b−4

b2⎛

⎝⎜

⎞

⎠⎟

5

23. a3

b2⎛

⎝⎜

⎞

⎠⎟

4

24. 2a3b−2

c3⎛

⎝⎜

⎞

⎠⎟

5

25. m−3n4

n−2⎛

⎝⎜

⎞

⎠⎟

4

26. p−3q−2

p−3q−3r5⎛

⎝⎜

⎞

⎠⎟

4

i i H8

FRACTION

Y 0

Y

a

F I SbkA

safe a i

a

i eni

EXAMPLE4:SIMPLIFYINGANEXPONENTIALEXPRESSIONSimplifyeachexpression.

27. 35⎛

⎝⎜⎞

⎠⎟−2

28. − 2xy

⎛

⎝⎜

⎞

⎠⎟

−4

29. − 323

⎛

⎝⎜

⎞

⎠⎟−2

30. x3y−2

z−5⎛

⎝⎜

⎞

⎠⎟

−4

31. r3s−1

r2s6⎛

⎝⎜

⎞

⎠⎟

−1

32. 213m14n22

m−2n−4p33r19⎛

⎝⎜

⎞

⎠⎟

0

33. 23⎛

⎝⎜⎞

⎠⎟−2

34. s−4

t−1⎛

⎝⎜

⎞

⎠⎟

−2

35. x−3yxz−4⎛

⎝⎜

⎞

⎠⎟

−2

36. x2y4z5

x−1y2z7⎛

⎝⎜

⎞

⎠⎟

−3x−2y2z−3

xy−5z−5⎛

⎝⎜

⎞

⎠⎟

4

455 fE FEET

y t.EEEf

FEETLEFTLyI