Question 1

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 11 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 4 } , \sqrt { 16 } \right\}$$
Whole numbers

Accepted Answer

A)  $11 , - 17,0$ 
B)  $11,0 , \frac { 0 } { 4 } , \sqrt { 16 }$ 
C)  11,0 
D)  $11 , - 17,0 , \sqrt { 16 }$ 
A)  $11 , - 17,0$ 
B)  $11,0 , \frac { 0 } { 4 } , \sqrt { 16 }$ 
C)  11,0 
D)  $11 , - 17,0 , \sqrt { 16 }$

Question 2

Find the sum or difference.
-$$( 2 x + 9 y ) ^ { 2 }$$

Accepted Answer

A)  $2 x ^ { 2 } + 81 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$ 
C)  $4 x ^ { 2 } + 81 y ^ { 2 }$ 
D)  $2 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$ 
A)  $2 x ^ { 2 } + 81 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$ 
C)  $4 x ^ { 2 } + 81 y ^ { 2 }$ 
D)  $2 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$

Question 3

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 7,8,9,10,11,12 \} , \mathrm { B } = \{ 9,11,13 \} , \mathrm { C } = \{ 7,8,10,12 \} , \mathrm { D } = \{ 7,12 \}$, and $\mathrm { U } = \{ 7,8,9,10,11,12,13 \}$. $\mathrm { B } \nsubseteq \mathrm { C }$

Accepted Answer

A) True 
 B)False

Question 4

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }$

Accepted Answer

A)  $\frac { \sqrt { 14 } - 1 } { 13 }$ 
B)  $\frac { \sqrt { 14 } + 1 } { 15 }$ 
C)  $\frac { \sqrt { 2 } + 1 } { 13 }$ 
D)  $\frac { \sqrt { 14 } + 1 } { 13 }$ 
A)  $\frac { \sqrt { 14 } - 1 } { 13 }$ 
B)  $\frac { \sqrt { 14 } + 1 } { 15 }$ 
C)  $\frac { \sqrt { 2 } + 1 } { 13 }$ 
D)  $\frac { \sqrt { 14 } + 1 } { 13 }$

Question 5

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 3 ^ { - 7 } } { 3 ^ { 8 } }$

Accepted Answer

A)  $\frac { 1 } { 615 }$ 
B)  $\frac { 1 } { 3 ^ { 56 } }$ 
C)  $\frac { 1 } { 3 ^ { 15 } }$ 
D)  $- 3 ^ { 15 }$ 
A)  $\frac { 1 } { 615 }$ 
B)  $\frac { 1 } { 3 ^ { 56 } }$ 
C)  $\frac { 1 } { 3 ^ { 15 } }$ 
D)  $- 3 ^ { 15 }$

Question 6

Factor, using the given factor. Assume all variables represent positive real numbers.
-$x ^ { 3 / 7 } + 3 x ^ { 2 / 7 } ; \quad x ^ { 2 / 7 }$

Accepted Answer

A)  $x ^ { 1 / 7 } \left( x ^ { 1 / 7 } + 3 \right)$ 
B)  $x ^ { 2 / 7 } \left( x ^ { - 1 / 7 } + 3 \right)$ 
C)  $x ^ { 2 / 7 } \left( x ^ { 1 / 7 } + 3 \right)$ 
D)  $x ^ { 1 / 7 } \left( x ^ { 3 / 7 } + 3 \right)$ 
A)  $x ^ { 1 / 7 } \left( x ^ { 1 / 7 } + 3 \right)$ 
B)  $x ^ { 2 / 7 } \left( x ^ { - 1 / 7 } + 3 \right)$ 
C)  $x ^ { 2 / 7 } \left( x ^ { 1 / 7 } + 3 \right)$ 
D)  $x ^ { 1 / 7 } \left( x ^ { 3 / 7 } + 3 \right)$

Question 7

Determine which property of absolute value justifies the statement.
-$| x | \geq 0$

Accepted Answer

A)  Property 5: the triangle inequality 
B)  Property 1: the absolute value of a number is positive or 0. 
C)  Property 1: the absolute value of a number is greater than 0. 
D)  Property 1: the absolute value of a number is positive. 
A)  Property 5: the triangle inequality 
B)  Property 1: the absolute value of a number is positive or 0. 
C)  Property 1: the absolute value of a number is greater than 0. 
D)  Property 1: the absolute value of a number is positive.

Question 8

Perform the indicated operations.
-$$\frac { 2 } { 3 x - 6 } - \frac { 1 } { 2 x + 2 } + \frac { 6 } { 5 x + 10 }$$

Accepted Answer

A)  $\frac { 71 x ^ { 2 } + 24 x + 28 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
B)  $\frac { 41 x ^ { 2 } + 24 x + 13 } { 10 x + 18 }$ 
C)  $\frac { 41 x ^ { 2 } + 24 x + 28 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
D)  $\frac { 71 x ^ { 2 } + 24 x + 28 } { 10 x + 18 }$ 
A)  $\frac { 71 x ^ { 2 } + 24 x + 28 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
B)  $\frac { 41 x ^ { 2 } + 24 x + 13 } { 10 x + 18 }$ 
C)  $\frac { 41 x ^ { 2 } + 24 x + 28 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
D)  $\frac { 71 x ^ { 2 } + 24 x + 28 } { 10 x + 18 }$

Question 9

Factor the polynomial by substitution.
-$$36 z ^ { 6 } + 87 z ^ { 4 } + 45 z ^ { 2 }$$

Accepted Answer

A)  $\left( 9 z ^ { 3 } + 15 \right) \left( 4 z ^ { 3 } + 3 \right)$ 
B)  $3 z ^ { 2 } \left( 4 z ^ { 2 } - 3 \right) \left( 3 z ^ { 2 } - 5 \right)$ 
C)  $3 \left( 3 z ^ { 4 } + 5 \right) \left( 4 z ^ { 2 } + 3 \right)$ 
D)  $3 z ^ { 2 } \left( 3 z ^ { 2 } + 5 \right) \left( 4 z ^ { 2 } + 3 \right)$ 
A)  $\left( 9 z ^ { 3 } + 15 \right) \left( 4 z ^ { 3 } + 3 \right)$ 
B)  $3 z ^ { 2 } \left( 4 z ^ { 2 } - 3 \right) \left( 3 z ^ { 2 } - 5 \right)$ 
C)  $3 \left( 3 z ^ { 4 } + 5 \right) \left( 4 z ^ { 2 } + 3 \right)$ 
D)  $3 z ^ { 2 } \left( 3 z ^ { 2 } + 5 \right) \left( 4 z ^ { 2 } + 3 \right)$

Question 10

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 3 ) ^ { - 1 }$

Accepted Answer

A)  $- 3$ 
B)  $\frac { 1 } { 3 }$ 
C)  $- \frac { 1 } { 3 }$ 
D)  3 
A)  $- 3$ 
B)  $\frac { 1 } { 3 }$ 
C)  $- \frac { 1 } { 3 }$ 
D)  3

Question 11

Evaluate the expression.
-Let $x = - 8 , y = 5$. Evaluate $| x + y |$.

Accepted Answer

A)  13 
B)  $- 13$ 
C)  $- 3$ 
D)  3 
A)  13 
B)  $- 13$ 
C)  $- 3$ 
D)  3

Question 12

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { m ^ { - 1 } + n ^ { - 1 } } { ( m n ) ^ { - 1 } }$$

Accepted Answer

A)  $n - m$ 
B)  $n + m$ 
C)  $- \mathrm { n } + \mathrm { m }$ 
D)  $- n - m$ 
A)  $n - m$ 
B)  $n + m$ 
C)  $- \mathrm { n } + \mathrm { m }$ 
D)  $- n - m$

Question 13

Factor the trinomial, if possible.
-$$( x - 2 y ) ^ { 2 } + 12 ( x - 2 y ) + 36$$

Accepted Answer

A)  $( x - 2 y - 6 ) ^ { 2 }$ 
B)  $( x + 2 y - 6 ) ( x - 2 y + 6 )$ 
C)  $( x + 2 y + 6 ) ^ { 2 }$ 
D)  $( x - 2 y + 6 ) ^ { 2 }$ 
A)  $( x - 2 y - 6 ) ^ { 2 }$ 
B)  $( x + 2 y - 6 ) ( x - 2 y + 6 )$ 
C)  $( x + 2 y + 6 ) ^ { 2 }$ 
D)  $( x - 2 y + 6 ) ^ { 2 }$

Question 14

Evaluate the expression.
-$$- 5 ( - 2 ) ^ { 3 }$$

Accepted Answer

A)  40 
B)  $- 1,000$ 
C)  $- 40$ 
D)  1,000 
A)  40 
B)  $- 1,000$ 
C)  $- 40$ 
D)  1,000

Question 15

Factor out the greatest common factor. Simplify the factors, if possible.
-$10 w x - 25 w y - 15 w z$

Accepted Answer

A)  $5 ( 2 w x - 5 w y - 3 w z )$ 
B)  $5 w ( 2 x - 5 y - 3 z )$ 
C)  $5 w ( 2 x - 25 w y - 15 w z )$ 
D)  $10 w ( x - 25 y - 15 z )$ 
A)  $5 ( 2 w x - 5 w y - 3 w z )$ 
B)  $5 w ( 2 x - 5 y - 3 z )$ 
C)  $5 w ( 2 x - 25 w y - 15 w z )$ 
D)  $10 w ( x - 25 y - 15 z )$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { \frac { 256 } { 81 } }$

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 16 } { 9 }$ 
C)  $\frac { 64 } { 27 }$ 
D)  $\frac { 256 } { 81 }$ 
A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 16 } { 9 }$ 
C)  $\frac { 64 } { 27 }$ 
D)  $\frac { 256 } { 81 }$

Question 17

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$- \left( \frac { 5 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }$$

Accepted Answer

A)  $- 1$ 
B)  $\frac { y ^ { 2 } } { 625 x ^ { 12 } }$ 
C)  $\frac { 625 x ^ { 12 } } { y ^ { 8 } }$ 
D)  1 
A)  $- 1$ 
B)  $\frac { y ^ { 2 } } { 625 x ^ { 12 } }$ 
C)  $\frac { 625 x ^ { 12 } } { y ^ { 8 } }$ 
D)  1

Question 18

Find the product or quotient.
-$\frac { 4 x ^ { 2 } } { 8 } \cdot \frac { 40 } { x ^ { 3 } }$

Accepted Answer

A)  $\frac { 20 } { x }$ 
B)  $\frac { 160 } { x }$ 
C)  $\frac { 20 } { x ^ { 2 } }$ 
D)  $20 \mathrm { x }$ 
A)  $\frac { 20 } { x }$ 
B)  $\frac { 160 } { x }$ 
C)  $\frac { 20 } { x ^ { 2 } }$ 
D)  $20 \mathrm { x }$

Question 19

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { 2 } - n ^ { 2 } }$$

Accepted Answer

A)  $\frac { 1 } { m n }$ 
B)  $\frac { 1 } { m + n }$ 
C)  $m + n$ 
D)  $m n$ 
A)  $\frac { 1 } { m n }$ 
B)  $\frac { 1 } { m + n }$ 
C)  $m + n$ 
D)  $m n$

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 27 }$

Accepted Answer

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

List all the elements of set B that belong to the indicated set. - $B = \left\{ 11 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 4 } , \sqrt { 16 } \right\}$ Whole numbers

Find the sum or difference. - $( 2 x + 9 y ) ^ { 2 }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 7,8,9,10,11,12 \} , \mathrm { B } = \{ 9,11,13 \} , \mathrm { C } = \{ 7,8,10,12 \} , \mathrm { D } = \{ 7,12 \}$ , and $\mathrm { U } = \{ 7,8,9,10,11,12,13 \}$ . $\mathrm { B } \nsubseteq \mathrm { C }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 ^ { - 7 } } { 3 ^ { 8 } }$

Factor, using the given factor. Assume all variables represent positive real numbers. - $x ^ { 3 / 7 } + 3 x ^ { 2 / 7 } ; \quad x ^ { 2 / 7 }$

Determine which property of absolute value justifies the statement. - $| x | \geq 0$

Perform the indicated operations. - $\frac { 2 } { 3 x - 6 } - \frac { 1 } { 2 x + 2 } + \frac { 6 } { 5 x + 10 }$

Factor the polynomial by substitution. - $36 z ^ { 6 } + 87 z ^ { 4 } + 45 z ^ { 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 3 ) ^ { - 1 }$

Evaluate the expression. -Let $x = - 8 , y = 5$ . Evaluate $| x + y |$ .

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m ^ { - 1 } + n ^ { - 1 } } { ( m n ) ^ { - 1 } }$

Factor the trinomial, if possible. - $( x - 2 y ) ^ { 2 } + 12 ( x - 2 y ) + 36$

Evaluate the expression. - $- 5 ( - 2 ) ^ { 3 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $10 w x - 25 w y - 15 w z$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 256 } { 81 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $- \left( \frac { 5 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }$

Find the product or quotient. - $\frac { 4 x ^ { 2 } } { 8 } \cdot \frac { 40 } { x ^ { 3 } }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { 2 } - n ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 27 }$

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Exam 1: Review of Basic Concepts

List all the elements of set B that belong to the indicated set. - B={11,5,−17,0,04,16}B = \left\{ 11 , \sqrt { 5 } , - 17,0 , \frac { 0 } { 4 } , \sqrt { 16 } \right\}B={11,5​,−17,0,40​,16​} Whole numbers

Find the sum or difference. - (2x+9y)2( 2 x + 9 y ) ^ { 2 }(2x+9y)2

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 772−7\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }72​−7​7​​

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 3−738\frac { 3 ^ { - 7 } } { 3 ^ { 8 } }383−7​

Factor, using the given factor. Assume all variables represent positive real numbers. - x3/7+3x2/7;x2/7x ^ { 3 / 7 } + 3 x ^ { 2 / 7 } ; \quad x ^ { 2 / 7 }x3/7+3x2/7;x2/7

Determine which property of absolute value justifies the statement. - ∣x∣≥0| x | \geq 0∣x∣≥0

Perform the indicated operations. - 23x−6−12x+2+65x+10\frac { 2 } { 3 x - 6 } - \frac { 1 } { 2 x + 2 } + \frac { 6 } { 5 x + 10 }3x−62​−2x+21​+5x+106​

Factor the polynomial by substitution. - 36z6+87z4+45z236 z ^ { 6 } + 87 z ^ { 4 } + 45 z ^ { 2 }36z6+87z4+45z2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−3)−1( - 3 ) ^ { - 1 }(−3)−1

Evaluate the expression. -Let x=−8,y=5x = - 8 , y = 5x=−8,y=5 . Evaluate ∣x+y∣| x + y |∣x+y∣ .

Perform the indicated operation and write your answer with positive integer exponents. - m−1+n−1(mn)−1\frac { m ^ { - 1 } + n ^ { - 1 } } { ( m n ) ^ { - 1 } }(mn)−1m−1+n−1​

Factor the trinomial, if possible. - (x−2y)2+12(x−2y)+36( x - 2 y ) ^ { 2 } + 12 ( x - 2 y ) + 36(x−2y)2+12(x−2y)+36

Evaluate the expression. - −5(−2)3- 5 ( - 2 ) ^ { 3 }−5(−2)3

Factor out the greatest common factor. Simplify the factors, if possible. - 10wx−25wy−15wz10 w x - 25 w y - 15 w z10wx−25wy−15wz

Simplify the expression. Assume all variables represent positive real numbers. - 256814\sqrt [ 4 ] { \frac { 256 } { 81 } }481256​​

Simplify the expression. Assume all variables represent nonzero real numbers. - −(5x3y2)0- \left( \frac { 5 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }−(y25x3​)0

Find the product or quotient. - 4x28⋅40x3\frac { 4 x ^ { 2 } } { 8 } \cdot \frac { 40 } { x ^ { 3 } }84x2​⋅x340​

Perform the indicated operation and write your answer with positive integer exponents. - m−1−n−1m2−n2\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { 2 } - n ^ { 2 } }m2−n2m−1−n−1​

Simplify the expression. Assume all variables represent positive real numbers. - 27\sqrt { 27 }27​