Download Chapter 7 Practice Test

Name: ______________________________
November 17, 2008
Chapter 7 Test (Sections 7.1-7.7 => show your work)
1.
(12 pts.) Find each root / simplify (assume all variables represent non-negative real numbers)
4 problems – (3 pts. each)
64 
3
8 
81x 6 
3
 27 x12 y 9 
2. (12 pts.) Use radical notation to write the following and simplify if possible.
4 problems – (3 pts. each)
271/3 =
5m2/3 =
(-8)4/3 =
(-64)-2/3 =
3. (3 pts.) Use the properties of exponents and multiplication to simplify x1/2(x1/2 – x3/2) =
4.
(3 pts.) Factor x3/2 from the expression x5/2 – x3/2 =
5. (6 pts.) Use rational exponents to simplify
2 problems – (3 pts. each)
6
y3 =
9
a 6b3 =
6. (3 pts.) Write
3
y
5
y 2 as a single radical expression with the same index.
7. (12 pts.) Use product / quotient rules as needed and simplify
4 problems – (3 pts. each)
5 75 
3
3

64
8. (3 pts.) Find the distance (hint: d 
9. (6 pts.) Add or subtract (and simplify)
2 problems – (3 pts. each)
3 45x 3  x 5x 
8
50


2
x
16 x 2
3
40 y 10 
a 7b6
a 3b 2

( x2  x1 ) 2  ( y 2  y1 ) 2 ) between (5,1) and (8,5).
10. (8 pts.) Multiply / simplify
2 problems – (4 pts. each)
( 5  5)( 2 5  2) 
3 ( 16  2 ) 
11. (6 pts.) Rationalize each denominator
2 problems – (3 pts. each)
2 3
y
45
2 3
12. (8 pts.) Solve each equation
2 problems – (4 pts. each)
x  x2 2
y 7  5
13. (3 pts.) Find x (use the Pythagorean Theorem)
3 cm
x
4 cm
14. (3 pts.) Suppose you’ve finally come to your senses and decided to show your love for VA Tech (not
the stinky Tide) by hoisting a beautiful Hokie flag in your yard on a 12 foot pole. Luckily, you have
13 feet of anchoring cable to connect the top of the pole to the ground. If you use all the cable,
how far from the base of the pole can you attach the cable to the ground (hint: you can set c to 13)?
15. (12 pts.) Perform each indicated operation. Write the result in the form of a + bi.
4 problems – (3 pts. each)
8 
(12  6i)  (12  3i) 
3   27 
(4 + 3i)2 =