Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 3 x } + 2 \sqrt { 108 x } + 4 \sqrt { 75 x }$

Accepted Answer

A)  $32 \sqrt { 3 x }$ 
B)  $6 \sqrt { 186 x }$ 
C)  $33 \sqrt { 3 x }$ 
D)  $7 \sqrt { 186 x }$ 
A)  $32 \sqrt { 3 x }$ 
B)  $6 \sqrt { 186 x }$ 
C)  $33 \sqrt { 3 x }$ 
D)  $7 \sqrt { 186 x }$

Question 2

Factor the trinomial, if possible.
-$2 x ^ { 2 } - 12 x + 16$

Accepted Answer

A)  $2 ( x - 2 ) ( x - 4 )$ 
B)  $2 ( x - 8 ) ( x + 1 )$ 
C)  $( x - 2 ) ( 2 x - 8 )$ 
D)  $( 2 x - 4 ) ( x - 4 )$ 
A)  $2 ( x - 2 ) ( x - 4 )$ 
B)  $2 ( x - 8 ) ( x + 1 )$ 
C)  $( x - 2 ) ( 2 x - 8 )$ 
D)  $( 2 x - 4 ) ( x - 4 )$

Question 3

Find the product or quotient.
-$$\frac { 4 p - 4 } { p } \div \frac { 5 p - 5 } { 2 p ^ { 2 } }$$

Accepted Answer

A)  $\frac { 5 } { 8 } \mathrm { p }$ 
B)  $\frac { 20 p ^ { 2 } + 40 p + 20 } { 2 p ^ { 3 } }$ 
C)  $\frac { 8 p ^ { 3 } - 8 p ^ { 2 } } { 5 p ^ { 2 } - 5 p }$ 
D)  $\frac { 8 } { 5 } p$ 
A)  $\frac { 5 } { 8 } \mathrm { p }$ 
B)  $\frac { 20 p ^ { 2 } + 40 p + 20 } { 2 p ^ { 3 } }$ 
C)  $\frac { 8 p ^ { 3 } - 8 p ^ { 2 } } { 5 p ^ { 2 } - 5 p }$ 
D)  $\frac { 8 } { 5 } p$

Question 4

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( \frac { 5 } { x } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 5 } { x ^ { 2 } }$ 
B)  $\frac { 25 } { x }$ 
C)  $25 x ^ { 2 }$ 
D)  $\frac { 25 } { x ^ { 2 } }$ 
A)  $\frac { 5 } { x ^ { 2 } }$ 
B)  $\frac { 25 } { x }$ 
C)  $25 x ^ { 2 }$ 
D)  $\frac { 25 } { x ^ { 2 } }$

Question 5

Find the sum or difference.
-$$[ ( 3 x - 4 ) + 4 y ] ^ { 2 }$$

Accepted Answer

A)  $9 x ^ { 2 } - 12 x + 16 + 12 x y + 16 y + 16 y ^ { 2 }$ 
B)  $9 x ^ { 2 } - 24 x + 16 + 24 x y - 32 y + 16 y ^ { 2 }$ 
C)  $9 x ^ { 2 } - 24 x + 16 + 12 x y + 16 y + 16 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 24 x + 24 x y - 32 y + 16 y ^ { 2 }$ 
A)  $9 x ^ { 2 } - 12 x + 16 + 12 x y + 16 y + 16 y ^ { 2 }$ 
B)  $9 x ^ { 2 } - 24 x + 16 + 24 x y - 32 y + 16 y ^ { 2 }$ 
C)  $9 x ^ { 2 } - 24 x + 16 + 12 x y + 16 y + 16 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 24 x + 24 x y - 32 y + 16 y ^ { 2 }$

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \sqrt { 9 } }$

Accepted Answer

A)  3 
B)  $\sqrt [ 5 ] { 9 }$ 
C)  $\sqrt [ 3 ] { 3 }$ 
D)  $\sqrt { 3 }$ 
A)  3 
B)  $\sqrt [ 5 ] { 9 }$ 
C)  $\sqrt [ 3 ] { 3 }$ 
D)  $\sqrt { 3 }$

Question 7

Evaluate the expression.
-$$\left[ - \frac { 3 } { 8 } - \left( - \frac { 1 } { 4 } \right) \right] - \left( \frac { 3 } { 2 } - \frac { 7 } { 8 } \right)$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { 5 } { 4 }$ 
C)  $- \frac { 3 } { 4 }$ 
D)  0 
A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { 5 } { 4 }$ 
C)  $- \frac { 3 } { 4 }$ 
D)  0

Question 8

Factor by any method.
-$$1000 s ^ { 3 } + 1$$

Accepted Answer

A)  $( 10 s - 1 ) \left( 100 s ^ { 2 } + 10 s + 1 \right)$ 
B)  $( 10 s + 1 ) \left( 100 s ^ { 2 } + 1 \right)$ 
C)  $( 10 s + 1 ) \left( 100 s ^ { 2 } - 10 s + 1 \right)$ 
D)  $( 1000 s + 1 ) \left( s ^ { 2 } - 10 s + 1 \right)$ 
A)  $( 10 s - 1 ) \left( 100 s ^ { 2 } + 10 s + 1 \right)$ 
B)  $( 10 s + 1 ) \left( 100 s ^ { 2 } + 1 \right)$ 
C)  $( 10 s + 1 ) \left( 100 s ^ { 2 } - 10 s + 1 \right)$ 
D)  $( 1000 s + 1 ) \left( s ^ { 2 } - 10 s + 1 \right)$

Question 9

Insert   in the blank to make the statement true.
-

Accepted Answer

A)  $\nsubseteq$ 
B)  $\subseteq$ 
A)  $\nsubseteq$ 
B)  $\subseteq$

Question 10

Find the sum or difference.
-$$\left( 7 n ^ { 6 } - 9 n + 2 n ^ { 3 } \right) + \left( 7 n ^ { 3 } + 6 n ^ { 6 } - 4 n \right)$$

Accepted Answer

A)  $13 n ^ { 6 } + 9 n ^ { 3 } - 13 n$ 
B)  $13 n + 9 n ^ { 6 } - 13 n ^ { 3 }$ 
C)  $- 3 n ^ { 6 } + 14 n ^ { 3 } - 2 n$ 
D)  $9 \mathrm { n } ^ { 10 }$ 
A)  $13 n ^ { 6 } + 9 n ^ { 3 } - 13 n$ 
B)  $13 n + 9 n ^ { 6 } - 13 n ^ { 3 }$ 
C)  $- 3 n ^ { 6 } + 14 n ^ { 3 } - 2 n$ 
D)  $9 \mathrm { n } ^ { 10 }$

Question 11

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-If the radius of a sphere is doubled, by what factor will the volume change?

Accepted Answer

A)  4 
B)  2 
C)  6 
D)  8 
A)  4 
B)  2 
C)  6 
D)  8

Question 12

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$\frac { | - 4 | } { | 5 | } = \left| \frac { - 4 } { 5 } \right|$

Accepted Answer

A) True 
 B)False

Question 13

Simplify the expression.
-$$\sqrt { ( 2 y - 8 ) ^ { 2 } }$$

Accepted Answer

A)  $- 2 y + 8$ 
B)  $2 | y | - 8$ 
C)  $2 y - 8$ 
D)  $2 y - 8 \mid$ 
A)  $- 2 y + 8$ 
B)  $2 | y | - 8$ 
C)  $2 y - 8$ 
D)  $2 y - 8 \mid$

Question 14

Find the sum or difference.
-$$\left( 3 x ^ { 9 } + 11 x ^ { 7 } - 4 x ^ { 3 } + 8 \right) - \left( 11 x ^ { 9 } - 8 x ^ { 5 } + 8 x ^ { 3 } - 9 \right)$$

Accepted Answer

A)  $8 x ^ { 9 } + 11 x ^ { 7 } - 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
B)  $8 x ^ { 9 } + 11 x ^ { 7 } + 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
C)  $- 8 x ^ { 9 } + 11 x ^ { 7 } - 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
D)  $- 8 x ^ { 9 } + 11 x ^ { 7 } + 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
A)  $8 x ^ { 9 } + 11 x ^ { 7 } - 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
B)  $8 x ^ { 9 } + 11 x ^ { 7 } + 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
C)  $- 8 x ^ { 9 } + 11 x ^ { 7 } - 8 x ^ { 5 } - 12 x ^ { 3 } + 17$ 
D)  $- 8 x ^ { 9 } + 11 x ^ { 7 } + 8 x ^ { 5 } - 12 x ^ { 3 } + 17$

Question 15

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( 9 \mathrm { k } ^ { 2 } \mathrm {~m} ^ { - 4 } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  $\frac { 2 k } { m ^ { 2 } }$ 
B)  $2 \mathrm {~km} ^ { 2 }$ 
C)  $3 \mathrm {~km} ^ { 2 }$ 
D)  $\frac { 3 k } { m ^ { 2 } }$ 
A)  $\frac { 2 k } { m ^ { 2 } }$ 
B)  $2 \mathrm {~km} ^ { 2 }$ 
C)  $3 \mathrm {~km} ^ { 2 }$ 
D)  $\frac { 3 k } { m ^ { 2 } }$

Question 16

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( 3 n ^ { 2 } \right) \cdot \left( 5 n ^ { 3 } \right)$$

Accepted Answer

A)  $8 n ^ { 5 }$ 
B)  $15  n ^ 5$ 
C)  $8 n ^ { 6 }$ 
D)  $15 \mathrm { n } ^ { 6 }$ 
A)  $8 n ^ { 5 }$ 
B)  $15  n ^ 5$ 
C)  $8 n ^ { 6 }$ 
D)  $15 \mathrm { n } ^ { 6 }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$3 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 64 a }$$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 64 a }$ 
B)  $12 \sqrt [ 3 ] { a }$ 
C)  $3 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 64 a }$ 
D)  $7 \sqrt [ 3 ] { a }$ 
A)  $4 \sqrt [ 3 ] { 64 a }$ 
B)  $12 \sqrt [ 3 ] { a }$ 
C)  $3 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 64 a }$ 
D)  $7 \sqrt [ 3 ] { a }$

Question 18

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { \left( x ^ { - 3 } \right) ^ { 0 } } { 6 x ^ { - 6 } }$$

Accepted Answer

A)  $\frac { x ^ { 9 } } { 6 }$ 
B)  $\frac { x ^ { 6 } } { 6 }$ 
C)  $6 x ^ { 6 }$ 
D)  0 
A)  $\frac { x ^ { 9 } } { 6 }$ 
B)  $\frac { x ^ { 6 } } { 6 }$ 
C)  $6 x ^ { 6 }$ 
D)  0

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt [ 3 ] { x ^ { 2 } y } \cdot \sqrt [ 3 ] { x } } { \sqrt [ 3 ] { y ^ { 2 } } }$$

Accepted Answer

A)  $\frac { x \sqrt [ 3 ] { y } } { y }$ 
B)  $\frac { x \sqrt [ 3 ] { y ^ { 2 } } } { y }$ 
C)  $x \sqrt [ 3 ] { y ^ { 2 } }$ 
D)  $x \sqrt [ 3 ] { \mathrm { y } }$ 
A)  $\frac { x \sqrt [ 3 ] { y } } { y }$ 
B)  $\frac { x \sqrt [ 3 ] { y ^ { 2 } } } { y }$ 
C)  $x \sqrt [ 3 ] { y ^ { 2 } }$ 
D)  $x \sqrt [ 3 ] { \mathrm { y } }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( 4 x ) ^ { - 3 }$

Accepted Answer

A)  $- 12 x$ 
B)  $- 64 x ^ { 2 }$ 
C)  $\frac { 1 } { 64 x ^ { 3 } }$ 
D)  $- \frac { 1 } { 12 x }$ 
A)  $- 12 x$ 
B)  $- 64 x ^ { 2 }$ 
C)  $\frac { 1 } { 64 x ^ { 3 } }$ 
D)  $- \frac { 1 } { 12 x }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 3 x } + 2 \sqrt { 108 x } + 4 \sqrt { 75 x }$

Factor the trinomial, if possible. - $2 x ^ { 2 } - 12 x + 16$

Find the product or quotient. - $\frac { 4 p - 4 } { p } \div \frac { 5 p - 5 } { 2 p ^ { 2 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( \frac { 5 } { x } \right) ^ { 2 }$

Find the sum or difference. - $[ ( 3 x - 4 ) + 4 y ] ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \sqrt { 9 } }$

Evaluate the expression. - $\left[ - \frac { 3 } { 8 } - \left( - \frac { 1 } { 4 } \right) \right] - \left( \frac { 3 } { 2 } - \frac { 7 } { 8 } \right)$

Factor by any method. - $1000 s ^ { 3 } + 1$

Insert in the blank to make the statement true. -

Find the sum or difference. - $\left( 7 n ^ { 6 } - 9 n + 2 n ^ { 3 } \right) + \left( 7 n ^ { 3 } + 6 n ^ { 6 } - 4 n \right)$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -If the radius of a sphere is doubled, by what factor will the volume change?

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\frac { | - 4 | } { | 5 | } = \left| \frac { - 4 } { 5 } \right|$

Simplify the expression. - $\sqrt { ( 2 y - 8 ) ^ { 2 } }$

Find the sum or difference. - $\left( 3 x ^ { 9 } + 11 x ^ { 7 } - 4 x ^ { 3 } + 8 \right) - \left( 11 x ^ { 9 } - 8 x ^ { 5 } + 8 x ^ { 3 } - 9 \right)$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( 9 \mathrm { k } ^ { 2 } \mathrm {~m} ^ { - 4 } \right) ^ { 1 / 2 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 3 n ^ { 2 } \right) \cdot \left( 5 n ^ { 3 } \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $3 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 64 a }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( x ^ { - 3 } \right) ^ { 0 } } { 6 x ^ { - 6 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { x ^ { 2 } y } \cdot \sqrt [ 3 ] { x } } { \sqrt [ 3 ] { y ^ { 2 } } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 4 x ) ^ { - 3 }$

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Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 3x+2108x+475x\sqrt { 3 x } + 2 \sqrt { 108 x } + 4 \sqrt { 75 x }3x​+2108x​+475x​

Factor the trinomial, if possible. - 2x2−12x+162 x ^ { 2 } - 12 x + 162x2−12x+16

Find the product or quotient. - 4p−4p÷5p−52p2\frac { 4 p - 4 } { p } \div \frac { 5 p - 5 } { 2 p ^ { 2 } }p4p−4​÷2p25p−5​

Simplify the expression. Assume all variables represent nonzero real numbers. - (5x)2\left( \frac { 5 } { x } \right) ^ { 2 }(x5​)2

Find the sum or difference. - [(3x−4)+4y]2[ ( 3 x - 4 ) + 4 y ] ^ { 2 }[(3x−4)+4y]2

Simplify the expression. Assume all variables represent positive real numbers. - 93\sqrt [ 3 ] { \sqrt { 9 } }39​​

Evaluate the expression. - [−38−(−14)]−(32−78)\left[ - \frac { 3 } { 8 } - \left( - \frac { 1 } { 4 } \right) \right] - \left( \frac { 3 } { 2 } - \frac { 7 } { 8 } \right)[−83​−(−41​)]−(23​−87​)

Factor by any method. - 1000s3+11000 s ^ { 3 } + 11000s3+1