Review for Test III – Sections 6.5-6.7,7.1-7.4
MAT135
Spring 2010
1. Divide and simplify: 16 x3  12 x 2  44 x  16  (4 x  4) .
2. Simplify:
3
72 x 7
. Assume that all variables represent positive real numbers.
125
3. Write as an exponential expression:
7
x4 .
4. Add and simplify: 9 63b2 a  2b 252a . Assume that all variables represent
positive real numbers.
5. Multiply and simplify: (4  2 3)(7  2) .
6. Divide and simplify:
28n 9
.
7n
7. Rationalize the denominator:
8. Solve for z:
9. Solve
1
.
5 7
2
1

z 9 z 5
1 1 1
  for x.
A w x
10. Simplify: 3 200  98  2 18.
11. Use division to determine if ( y  3) is a factor of y 2  7 y  12 .
12. Simplify: (2 x  3)2 .
13. For x visits to an aquarium, the cost per visit is represented by
$175
 $1.95 . Write
x
this as a single rational expression. What is the cost of 4 visits to the aquarium?
14. What is the domain, in interval notation, of f ( x)  4  x ?
Dugopolski
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Review for Test III – Sections 6.5-6.7,7.1-7.4
MAT135
15. Simplify:
32 x8
x6 z 7
Spring 2010
z9
.
4
16. Are the following statements true or false?
a.
x 2  16  x  4 .
b.
16 x  4 x
c. ( x 
y )2  x  y .
d. (3 2)( 3)  3 6
17. If f ( x)  5 x 27 x and g ( x)  4 3 x 3 , find
a. f(x) + g(x).
b. f(x) - g(x).
18. Find the area of a rectangle whose length is
inches.
19. Rationalize the denominator and simplify:
20. Solve: 9 
Dugopolski
5 inches and whose width is 2 5
a b
.
a b
8 20

.
p p2
2
Review for Test III – Sections 6.5-6.7,7.1-7.4
MAT135
Spring 2010
Answer Key
1) 4x2 – 7x – 4
2)
2 x2 3
9x
5
3)
x7
4
4) 39b 7a
5) 28  4 2  14 3  2 6
6) 2n 4
7)
5 7
18
8) z = 19
9)
x
Aw
w A
10) 29 2
11) No
12) 4 x  12 x  9
13) $182.80
14) (, 4]
15) 2 xz 2
16) a) F
b)F
c)F
d)T
17) a) 19 x 3x
b) 11x 3 x
18) A = 10
a  2 ab  b
a b
10
20) p=– 2 , p 
9
19)
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