Algebra 2 Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 148

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Section 5.1-5.4 Review Packet

Section 5.1

Find the indicated real nth root(s) of a.

1. 3, 343n a 2. 6, 64n a �

Evaluate the expression without using a calculator.

3. 3 236 4. 3 416 5. � �2 532�

6. � �5 3125� 7. 5 4256�

Find the radius of the figure with the given volume.

8. 3425 in.V 9. 31458 mV

Find the real solution(s) of the equation.

10. 46 60x 11. 5 233x � 12. 415 125x 13. 31

7 49x �

Section 5.2

In Exercises 1–5, use the properties of rational exponents to simplify the expression.

1. 2 522

2. 1 66

63

12

�§ ·¨ ¸© ¹

3. � � 1 35 23 211 11��

x

4. � � 13 5 1 59 9�� x 5.

3 43 4

3 43 27

9x

Use the properties of radicals to simplify the expression.

6. 5 56 81x 7. 4

4

17611

8. 7700

9. 3 3

3

5 502

x

# =7

noreofohtion(F) 3=216 4*3=8

East chariot,IEFH

'

42s=fiTr2h1275 = TMA )

TT182.14 =Tr2

Fit

FIRE

TT f) ( hT J 45×4=4627¥-3.3434#IF X 'FF3

×=±s ×=. ,

x=±'if

%=j' 15

= ,3÷,=l÷=44i"5

"'

( ii'j"3=1/43.

FYFE*ftp.F

54586

speiss .

"

F6=2 ftoefoo10

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Resources by Chapter

149

Write the expression in simplest form.

10. 3425

11. 42401

4 12. 7

5 3� 13. 2

15 3�

Simplify the expression.

14. 2 54 11 6� 15. 3 313 3 375� 16. � � � �1 4 1 44 48 3 3�

Section 5.3

Describe the transformation of f represented by g. Then graph each function. Identify the domain and range of the function.

1. � � � �; 1 4f x x g x x � � 2. � � � �3 3; 2f x x g x x � 10.

3. � � � �4 4; 1 3f x x g x x � � � 4.. � � � �1 3 1 312; 3f x x g x x �

=# ( Str )s ( Str )

¥s¥d=÷Es ¥s¥s#estr22

133kt ?n 4ft . if13k - 5 't

8 't

IT:L.IE#xoontranslation•

right I

Dax:|€

R=y24d

• ReflectionK tix - ]

a across xaxis:#thptrinslatn@TifhEnYiaHI-oh.trandatmyTi.R

right 1

RTR

D= XzlR=yE3

Algebra 2 Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 150

Write a rule for g described by the transformations of the graph of f.

5. Let g be a vertical shrink by a factor of 13, followed by a translation 3 units right of the graph of

� � 5.f x x �

6. Let g be a reflection in the x-axis, followed by a translation 2 units down of the graph of � � 5 3.f x x �

7. Let g be a horizontal stretch by a factor of 2, followed by a translation 2 units up of the graph of � � 3 .f x x

8. Let g be a translation 1 unit up and 4 units left, followed by a reflection in the y-axis of the graph of � � 1

2.f x x � �

Section 5.4

Solve the equation. Check your solution(s).

1. 343 0x � 2. 53 9 15x � 3. 4 8 16 12x � �

4. 10 24 12x x� � 5. 4 22 25 5x x� 6. 4 4 8 0x x� � �

7. 3 34 1 6 5x x� � 8. 2 33 30 18x � 9. � �1 26 8 3 0x x� �

frxts gktstrxtstsgcxtstfxs[ ) - six - 3-2 gkk - Six -5

3F⇒=Fxt2 gcxf @ +2

gkttx -1+1

g(×)=-xt4-t£+ lltlb

*:# limit.Hirota 8¥2111=3/16 × - 32

( Hp ( ICY10×+24=4+12*+12) 2-25×2=625×4 (54×-45--6+8)

'

10×+242×424×+1440=625×4+25×424*4=5+8

0=5+14×+120 0=(25×2-1)(25×2+I 3×-4+4=8+4

no real 0=6*5*25×42) ¥t¥solutions X= -5,45

.tn#sxIsIEoygxt4

JX 2

3×43=48 ¢6xtA'¥341 '

3×197%443*634

6×+8=4'

-

4th×= a 0=9×2-6×-8 -12×2

0=(3×+2×3×-4)

1,72x= 64

x= -213,41, 3¥,4,186,12

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151

solve the inequality.

10. 4 3 23x � d 11. 10 6x � t 12. 3 2 15x� � �

D= xztaD=x-> -2

Dtxzo |#( Ki

as1/+10=36 ( red

'

-4'oEt¥¥¥sI

* 26x¥Eg