8-4:MOREMULTIPLICATIONPROPERTIESOFEXPONENTS

LessonObjectives:• Raiseapowertoapower• Raiseaproducttoapower

PROPERTY:RAISINGAPOWERTOAPOWERForeverynonzeronumberaandintegersmandn,a) 54( )

2 b) x2( )−5

EXAMPLE1:SIMPLIFYINGAPOWERRAISEDTOAPOWERSimplifyeachexpression.1. x3( )

6 2. 2−3( )4 3. s2( )

2 4. d 2( )−4

5. a4( )

6 6. b−3( )2 7. m−5( )

−3 8. y7( )−4

Besuretousetheorderofoperationstosimplifytheexpressionsinparenthesesfirst.EXAMPLE2:SIMPLIFYINGANEXPRESSIONWITHPOWERSSimplifyeachexpression.9. c5 c3( )

2 10. 25 24( )−2 11. x4 x4( )

3 12. a4( )−5•a13

fiypoawe.roerMultiply xD4x34x

amn am.n

5 Its j

x

iq4b 32

yC41

bgmm

ya

ECb 25.28 X x A20ab23 of

13. y21 y6( )−3 14. n6 n−2( )

5 15. b2( )4•b−9 16. d3 d 2( )

5 17.Findthevalueofaif: 18.Findthevalueofa,b,andcif: x−5 xa( )

3= x16 a x2( )

3y4( )

5•−4 xb( )

4y−2( )

c=12x2y30

PROPERTY:RAISINGAPRODUCTTOAPOWERForeverynonzeronumbersaandbandintegern,a) 3x( )4 EXAMPLE3:SIMPLIFYINGAPRODUCTRAISEDTOAPOWERSimplifyeachexpression.19. 4a5( )

3 20. m−3n4( )−4 21. x2y( )

4 22. 4−1s3( )−2

23. x4y( )

3 24. 12b−2( )2 25. 5a3b5( )

4 26. −16x−2y−7z3( )0

y j n ri b8ba d d

Y h

s 3a X f4a 1 4 4b yo y24 1228Esta I f4a 4btt

gactor l2X2y

zg 34232 4b KIIEEIgy

Sx SX 5XK5 s s s Lx x x 53 3 12511

ab n anb

344 81 4

a a i

x4Pyy

2 b a2

14454 is

EXAMPLE4:SIMPLIFYINGAPRODUCTRAISEDTOAPOWERSimplifyeachexpression. 27. x−2( )

23xy2( )

4 28. 4x4( ) 2xy3( )2 29. x−4( )

5x3y2( )

5 30. 3 f 4g−3( ) f 2g−2( )−1

31. x5y3( )

3xy5( )

2 32. m5( )−3m4n5( )

4 33. a3b4( )−2a−3b−5( )

−4 34.Finda,b,andcifax2ybz3( )

23x4y2z2( )

c=25y4z4

3

EXAMPLE5:RAISINGSCIENTIFICNOTATIONTOAPOWERSimplify.Writeeachexpressioninproperscientificnotation.35. 3×10−6( )

3 36. 5×102( )−3 37.10−3 2×103( )

5 39. 9×107( )

2 40. 3×105( )4 41.105 8×107( )

3

434 44,8 4 4 4246 zf4g3 f2g81 08 µ 6y II'sy zfag i8 Y 3

x.yxjm mm a b

a2 4y2bz6 5 44,257 2544243A z 25

34ct4 o y2bt2c y4z2 z

26 241 42b 2b

33 1018 53 106 103.25 10s

2z o set x 0 b 32 10121

ns7xiof 3.2

92 1014 34 1020 ios 83102

gj j4t 84102 qg 10262

8y i8il 1 qy