Radicals, Logarithmic and Exponential Functions

1 ) Simplify replace all radicals with rational exponents ? [25x8y6] [25x8y6]1 /2 [52x8y6]1 /2 5x4y3

2 ) Change to radical form (3ab )4 /9 9 ([ (3ab ) 4] 3 ) Evaluate or simplify (27y9 )-1 /3 [33 (y3 )3 ]-1 /3 [1 33 (y3 )3 ]1 /3 1 /3y3

4 ) Simplify ?[32x7y2] ([ (2 )5x7 y2] 22x3y ([2x] 4x3y ([2x]

5 ) Simplify : 3 ? [54x8y6] 3 ([2 (3 )3 (x2 )3 (y2 )3 (x2 )] (3x2y2 ( 3 ([2x2]

6 ) Combine ? [5x3] x ? [125x] x ([5x] 5x ([5x] 6x ([5x] 7 ) Multiply and simplify assume that all variables represent

nonnegative real numbers (2 ? [7] ? [2] (3 ? [7] - 4 ? [2] (2 ([7] (3 ([7] ) - (2 ([7] (4 ([2] ([2] (3 ([7] ) - ([2] (4 ([2] 6 (7 ) - 8 ([14] 3 ([14] - 4 (2 42 - 8 (- 8 3 ([14] 34 - 5 ([14]

8 ) Multiply and simplify ? [4x 1] 2 )2 ([4x 1] )2 (2 )2 2 (2 ([4x 1] (4x 1 4 4 ([4x 1] 4x 4 ([4x 1] 5

9 ) Simplify by rationalizing the denominator ?[6] - ?[3] ?[6] ?[3] ([6] - ([3] ([6] - ([3] ([6] ([3] ([6] - ([3] ([6] 2 ([3] 2 2 ([6] ([3] ([6] 2 - ([3] 2 6 3 2 (18

6 - 3 9 6 (2

3 3 2 (2 ? [- 2] ? [-5] 2i ( 5i 10 (i )2 10 (- 1 - 10

11 ) Perform the addition and subtraction : [ (1 /3 (2 /3 )i] [ (1 /3 ) - (5 /6 )i] [ (1 /3 (1 /3 )] [ (2 /3 ) - (5 /6 )]i (2 /3 (- 1 /6 )i (2 /3 ) - (1 /6 )i

12 ) Divide : -12i (2 - 5i -12i (2 5i (2 - 5i (2 5i -24i - 60 (i )2 (2 )2 - (5i )2 -24i 60

4 25

4

6

l

n

p

d

zh

-

2

4

`

h

j

l

n

p

t

-

ZH

K

M

F

TZ

SH

YU

a

w

d

f

h

j (R

yu

D

F

H

J

L

P

R

V

X

Z

`

b

d

f

h

j

n (R

YU ?4YU

a

w

zh

i

o

t

f

tz ?V - (24 /29 )i (60 /29

13 ) Solve for x : 11x 1 (11 ) x (11 )0

x 0

14 ) Solve for x : 3-x 1 / 81

3- x (1 /3 ) 4

3- x 3- 4

-x -4

x 4

15 ) Solve for x : 33x 4 27

3 (3x 4 (3 )3

3x 4 3 3x - 1

x - 1 /3

16 ) Write in exponential form : 4 log2 16 (2 )4 16

17 ) Solve : log3 (1 /81 y

3y (1 /81

3y (1 /3 )4

3y (3 ) - 4

y - 4

18 ) Express as a product : log7 4 ?[y] [log7 (y ) 1 /2]4 (1 /2 )4 . [log7 (y )] 4

19 ) Write as the sum or difference of single logarithms of a , b , and x

log6 (2b5 ?[a] /x3 log6 (2b5 log6 ? [a] ) - log6 (x3 5 log6 (2b 1 /2 log6 (a ) - 3 log6 (x...