comalge prac ex2 june 2012

7/27/2019 Comalge Prac Ex2 June 2012

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COMALGE PRACTICE EXERCISE 2

I. Find the value of each of the following:

a. 25

4b. 2

3

16 c. 3264 d. 35)27( e. 4381 f. 3

2

125

8 g. 8

34)25(

II. Simplify the give answers in positive exponent only

a.31

5

1

6

1

yx3yx7

2

b. ( ) 31129yx27 c. ( ) ( ) 3121 6046 yx27yx16 d. 2152

31

53

yx8

yx16

e. 31

9023

46)yx64()yx25(

f.32

43

231

yx12

yx8

g.

4

21

21

21

32

ba

ba

h.51

75

35

ba2431

i.

6

21

32

n

m

j.3

2

6

3

yx27

yx8 34

k.2

1

1

30

32

ba25

ba36

l.b

4b2

2b1

2b1

x

x

+

m.5

1

35

6

4565

yx243

yx

n.a

a

b3a

x

x + b

b2

b2a

x

x

o. 2b2ab

b4

b5a

x

x

III. Perform the indicated operations

a.

4x3x4x5 4

1

43

b. + 21

21

21

21

bab4a3 c.

+

21212121 n5m2n5m2

d.2

21

21

yx4

e. 23131 y3x

+ f. ( )32210 g. ( )( )3352345 + h. ( )( )y2xy2x i. + 33 23 23 nmnm j. ( )333 23 2 yxyx + k. 125207803452 + l. 333 12822165 m. 33 16312542274 + n. 3 573 423 543 5 dcdc27dc27dc8 o.

3 4

3 22

3 4ab3

ba

1ba + p. yx3)yx(92)yx(4 +

q.ba

ba

ba

ba ++ r. 3 53 83 423 24 mg27gm24mg8mg3 + s. 3 63 25 xy10yx16COMALGE PRACTICE EXERCISE 2

t. 4 1054 96 nm20nm28 u. 223223 v.4 2

4 3

ab8

ba24

w. 7543 ba72ba8 x. 3 5374 yxyx y. 4 833 46 ba18ba36IV. Simplify each of the following radicals

a. 85yx63 b. 3 510ba81 c.4 912yx48

d. 5 18107 yx3 e. 6 22nm f.3 4 9a

1


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g. 6 68yx h. 3 6)yx2(27 + i. 56 )ab(x

j. 8 66 )vu(3 + k.mn2

nm324 97

l.x

96x +

V. Rationalize the denominator

a. 7

2

b.3

9

4

c. x3

5

d. 4 3yx

a3

e.5

3

2

y16

x7

f. 3142

125

yx4

yx27g.

5 2

53

yx8

yx8h.

32

7

i. 2102

+ j. 3532

+

k.255

235

l.3273

327

+

m.3y2

y3

n. 4y2y

2

2

+o.

x6x

x

2 p. 33 ba4

+VI. Perform the indicated operations.

1. 27 2. 32 3. 50 4. 47i

5. 162i 6.90

i 7. )i4()i23( + 8. )i32)(i32( +9. )931)(93( 10.

i3

i2 11.

i23

i13+ 12. i7 i4814 +

13.i51

)i2)(i23( + 14. i2i43

i2

i43 +++ 15. 6)i2(3)i2( 2

16. )i43)(i43( + 17.i23

i51

i51

i23 ++ 18. Find 74x10x2 + if i75x + COMALGE PRACTICE EXERCISE 2

VII. Find the solution set of each equation. Check if necessary.

1. 223

x2

4

x35 + 8.

t3

1t2

2t3

3t2 =

2.4

5x6

2

1x3

5

x +=+ 9.2x

3

4x5

5

3x2

4 3.

3x

3x24

3x

x = 10. 3x6 53x2 12x3 4 +4.

5

3y27y3

2

7y3 += 11.9x3x2

3

3x

3

3x2

12 =+

5.1p6

5p3

1p4

5p2 +=++ 12. 1xx2 6x121x 41x2 5 2 +=+2


3/3

6.1x

2

1x6

11 ++ 13. 2x 9x43x2 9x8)1x)(3x2( 7x ++=++

7.8y9

1y6

4y3

1y2 =++ 14. 5x36x6

5x

7x2

)1x)(5x3(

20x5

=++

VIII. Solve for the letters indicated.

1. x;)ax(35)4ax(2 5. o2o v;tg2

1tvS +

2. 121 b;h)bb(2

1A + 6. a;bc2ac2ab2A +

3. L;r1

rLaS = 7. f;1f25FLM +

4.n;d)1n(aL 8. 221 d;d

1

d

1

f

1 +IX. Solve the following quadratic equations by factoring (if applicable), by completing the square and by

quadratic formula.

1. 10xx3 2 = 5. 02x3x2 2 = 9. 012x5x2 2 =2. 09x12x4 2 = 6. 0x4x 2 = 10. 02x2x 2 =3. 01x8x4 2 = 7. 7x6x2 2 + 11. 04x13x2 2 =4. 013x4x2 = 8. 036x 2 = 12. 04x3 2 =

3

comalge prac ex2 june 2012

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