8-5: DIVISION PROPERTIES OF EXPONENTS · 8-5: DIVISION PROPERTIES OF EXPONENTS Lesson Objectives:...
Transcript of 8-5: DIVISION PROPERTIES OF EXPONENTS · 8-5: DIVISION PROPERTIES OF EXPONENTS Lesson Objectives:...
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