Question 1

Write in radical form. Assume all variables represent positive real numbers.
-$2 x ^ { 1 / 3 }$

Accepted Answer

A)  $\sqrt [ 1 / 3 ] { 2 x }$ 
B)  $\sqrt [ 3 ] { 2 x }$ 
C)  $2 \sqrt [ 3 ] { x }$ 
D)  $\frac { 2 } { \sqrt [ 3 ] { x } }$ 
A)  $\sqrt [ 1 / 3 ] { 2 x }$ 
B)  $\sqrt [ 3 ] { 2 x }$ 
C)  $2 \sqrt [ 3 ] { x }$ 
D)  $\frac { 2 } { \sqrt [ 3 ] { x } }$

Question 2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 9 + \frac { 3 } { s } } { \frac { s } { 4 } + \frac { 1 } { 12 } }$$

Accepted Answer

A)  $\frac { 36 } { \mathrm {~s} }$ 
B)  36 
C)  $\frac { s } { 36 }$ 
D)  1 
A)  $\frac { 36 } { \mathrm {~s} }$ 
B)  36 
C)  $\frac { s } { 36 }$ 
D)  1

Question 3

Decide whether the expression has been simplified correctly.
-$4 ^ { 0 } x = x$

Accepted Answer

A)  Simplified correctly 
B)  Not simplified correctly 
A)  Simplified correctly 
B)  Not simplified correctly

Question 4

Decide whether the expression has been simplified correctly.
-$\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 6 }$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Question 5

Find the domain of the expression.
-$$\frac { 2 x - 3 } { ( 4 x - 3 ) ( x + 6 ) }$$

Accepted Answer

A)  all real numbers 
B)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 4 } , - 6 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq x - \frac { 3 } { 4 } , 6 \right\} \right.$ 
D)  $\left\{ \left\{ x \mid x \neq \frac { 4 } { 3 } , - 6 \right\} \right.$ 
A)  all real numbers 
B)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 4 } , - 6 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq x - \frac { 3 } { 4 } , 6 \right\} \right.$ 
D)  $\left\{ \left\{ x \mid x \neq \frac { 4 } { 3 } , - 6 \right\} \right.$

Question 6

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

Accepted Answer

A)  $12 x ^ { 12 } + 8 x ^ { 8 }$ 
B)  $12 x ^ { 8 } - 8 x ^ { 6 }$ 
C)  $12 x ^ { 8 } + 8 x ^ { 6 }$ 
D)  $12 x ^ { 8 } + 4 x ^ { 4 }$ 
A)  $12 x ^ { 12 } + 8 x ^ { 8 }$ 
B)  $12 x ^ { 8 } - 8 x ^ { 6 }$ 
C)  $12 x ^ { 8 } + 8 x ^ { 6 }$ 
D)  $12 x ^ { 8 } + 4 x ^ { 4 }$

Question 7

Find the sum or difference.
-$$( x + 4 ) ( - 3 x - 2 )$$

Accepted Answer

A)  $- 3 x ^ { 2 } - 8 x - 14$ 
B)  $- 3 x ^ { 2 } - 16 x - 8$ 
C)  $- 3 x ^ { 2 } - 14 x - 14$ 
D)  $- 3 x ^ { 2 } - 14 x - 8$ 
A)  $- 3 x ^ { 2 } - 8 x - 14$ 
B)  $- 3 x ^ { 2 } - 16 x - 8$ 
C)  $- 3 x ^ { 2 } - 14 x - 14$ 
D)  $- 3 x ^ { 2 } - 14 x - 8$

Question 8

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 2,3,4,5,6,7,8,9,10,11,12 \} , \mathrm { M } = \{ 2,4,6,8 \} , \mathrm { N } = \{ 3,5,7,9,11 \} , \mathrm { Q } = \{ 2,4,6,8,10,12 \}$, and $\mathrm { R } = \{ 2,3,4,5 \}$.
Q $\cap R ^ { \prime }$

Accepted Answer

A)  $\{ 5,6,7,8,9,10,11,12 \}$ 
B)  $\varnothing , Q$ and $R ^ { \prime }$ are disjoint sets. 
C)  $\{ 4,6,8,10,12 \}$ 
D)  $\{ 6,8,10,12 \}$ 
A)  $\{ 5,6,7,8,9,10,11,12 \}$ 
B)  $\varnothing , Q$ and $R ^ { \prime }$ are disjoint sets. 
C)  $\{ 4,6,8,10,12 \}$ 
D)  $\{ 6,8,10,12 \}$

Question 9

Use set notation, and list all the elements of the set.
-{19, 20, 21, . . . , 25}

Accepted Answer

A)  {19, 20, 22, 24, 25} 
B)  {19, 21, 23, 25} 
C)  {19, 20, 21, 22, 23, 24, 25} 
D)  {19, 20, 21, 22, 23, 24, 25, 26} 
A)  {19, 20, 22, 24, 25} 
B)  {19, 21, 23, 25} 
C)  {19, 20, 21, 22, 23, 24, 25} 
D)  {19, 20, 21, 22, 23, 24, 25, 26}

Question 10

Find the product or quotient.
-$$\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 14 k + 48 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 12 k + 35 }$$

Accepted Answer

A)  $\frac { \mathrm { k } ^ { 2 } + 8 \mathrm { k } } { \mathrm { k } + 7 }$ 
B)  $\frac { 1 } { \mathrm { k } + 7 }$ 
C)  $\frac { k } { k ^ { 2 } + 14 k + 48 }$ 
D)  $\frac { \mathrm { k } } { \mathrm { k } + 7 }$ 
A)  $\frac { \mathrm { k } ^ { 2 } + 8 \mathrm { k } } { \mathrm { k } + 7 }$ 
B)  $\frac { 1 } { \mathrm { k } + 7 }$ 
C)  $\frac { k } { k ^ { 2 } + 14 k + 48 }$ 
D)  $\frac { \mathrm { k } } { \mathrm { k } + 7 }$

Question 11

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 5 r ^ { - 1 } \left( r ^ { 3 } \right) ^ { 4 } } { 2 \left( r ^ { - 2 } \right) ^ { - 2 } }$

Accepted Answer

A)  $\frac { 5 } { 2 r ^ { 7 } }$ 
B)  $\frac { 5 r ^ { 10 } } { 2 }$ 
C)  $\frac { 5 } { 2 r ^ { 10 } }$ 
D)  $\frac { 5 r ^ { 7 } } { 2 }$ 
A)  $\frac { 5 } { 2 r ^ { 7 } }$ 
B)  $\frac { 5 r ^ { 10 } } { 2 }$ 
C)  $\frac { 5 } { 2 r ^ { 10 } }$ 
D)  $\frac { 5 r ^ { 7 } } { 2 }$

Question 12

Factor by any method.
-$$( 3 x - 2 ) ^ { 2 } - y ^ { 2 }$$

Accepted Answer

A)  $( 3 x + 2 + y ) ( 3 x + 2 - y )$ 
B)  prime 
C)  $( 3 x - 2 + y ) ( 3 x - 2 - y )$ 
D)  $( 3 x - 2 + y ) ( 3 x + 2 - y )$ 
A)  $( 3 x + 2 + y ) ( 3 x + 2 - y )$ 
B)  prime 
C)  $( 3 x - 2 + y ) ( 3 x - 2 - y )$ 
D)  $( 3 x - 2 + y ) ( 3 x + 2 - y )$

Question 13

Find the sum or difference.
-$$( n - 2 ) ( n - 2 ) ( n + 2 ) ( n + 2 )$$

Accepted Answer

A)  $n ^ { 4 } + 8 n - 16$ 
B)  $n ^ { 4 } + 8 n ^ { 2 } - 16$ 
C)  $n ^ { 4 } - 8 n + 16$ 
D)  $n ^ { 4 } - 8 n ^ { 2 } + 16$ 
A)  $n ^ { 4 } + 8 n - 16$ 
B)  $n ^ { 4 } + 8 n ^ { 2 } - 16$ 
C)  $n ^ { 4 } - 8 n + 16$ 
D)  $n ^ { 4 } - 8 n ^ { 2 } + 16$

Question 14

Find the product. Assume variables represent positive real numbers.
-$y ^ { 1 / 3 } \left( y ^ { 4 / 9 } - 4 y ^ { 2 / 9 } \right)$

Accepted Answer

A)  $y ^ { 4 / 27 } - 4 y ^ { 2 / 27 }$ 
B)  $y ^ { - 1 / 9 } - 4 y ^ { 1 / 9 }$ 
C)  $y ^ { 7 / 9 } - 4 y ^ { 5 / 9 }$ 
D)  $y ^ { 3 / 4 } - 4 y ^ { 3 / 2 }$ 
A)  $y ^ { 4 / 27 } - 4 y ^ { 2 / 27 }$ 
B)  $y ^ { - 1 / 9 } - 4 y ^ { 1 / 9 }$ 
C)  $y ^ { 7 / 9 } - 4 y ^ { 5 / 9 }$ 
D)  $y ^ { 3 / 4 } - 4 y ^ { 3 / 2 }$

Question 15

Factor by any method.
-$$( q - 4 ) ^ { 2 } - 9$$

Accepted Answer

A)  $( q - 1 ) ( q - 7 )$ 
B)  $( q + 7 ) ( q - 7 )$ 
C)  $( q - 1 ) ^ { 2 }$ 
D)  $\left[ ( q - 4 ) ^ { 2 } + 3 \right] \left[ ( q - 4 ) ^ { 2 } - 3 \right]$ 
A)  $( q - 1 ) ( q - 7 )$ 
B)  $( q + 7 ) ( q - 7 )$ 
C)  $( q - 1 ) ^ { 2 }$ 
D)  $\left[ ( q - 4 ) ^ { 2 } + 3 \right] \left[ ( q - 4 ) ^ { 2 } - 3 \right]$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 12 } + \sqrt { 8 } ) ( \sqrt { 12 } - \sqrt { 8 } )$

Accepted Answer

A)  4 
B)  $12 + 2 \sqrt { 96 }$ 
C)  20 
D)  $12 - 8 \sqrt { 24 }$ 
A)  4 
B)  $12 + 2 \sqrt { 96 }$ 
C)  20 
D)  $12 - 8 \sqrt { 24 }$

Question 17

Factor out the greatest common factor. Simplify the factors, if possible.
-$$5 t ^ { 2 } - 10 t - 25$$

Accepted Answer

A)  $5 \left( t ^ { 2 } - 10 t - 25 \right)$ 
B)  $5 t \left( t ^ { 2 } - 2 t - 5 \right)$ 
C)  $5 \left( t ^ { 2 } - 2 t - 5 \right)$ 
D)  $5 \left( t ^ { 2 } - 5 t - 20 \right)$ 
A)  $5 \left( t ^ { 2 } - 10 t - 25 \right)$ 
B)  $5 t \left( t ^ { 2 } - 2 t - 5 \right)$ 
C)  $5 \left( t ^ { 2 } - 2 t - 5 \right)$ 
D)  $5 \left( t ^ { 2 } - 5 t - 20 \right)$

Question 18

Find the product. Assume variables represent positive real numbers.
-$$- 9 k ^ { 1 / 8 } \left( 8 k ^ { 3 / 8 } - 5 k ^ { 3 / 4 } \right)$$

Accepted Answer

A)  $- 72 k ^ { 1 / 2 } - 45 k ^ { 7 / 8 }$ 
B)  $- 72 k ^ { - 1 / 4 } - 45 k ^ { - 5 / 8 }$ 
C)  $- 72 \mathrm { k } ^ { 1 / 2 } + 45 \mathrm { k } ^ { 7 / 8 }$ 
D)  $- 72 k ^ { 3 / 64 } + 45 k ^ { 3 / 32 }$ 
A)  $- 72 k ^ { 1 / 2 } - 45 k ^ { 7 / 8 }$ 
B)  $- 72 k ^ { - 1 / 4 } - 45 k ^ { - 5 / 8 }$ 
C)  $- 72 \mathrm { k } ^ { 1 / 2 } + 45 \mathrm { k } ^ { 7 / 8 }$ 
D)  $- 72 k ^ { 3 / 64 } + 45 k ^ { 3 / 32 }$

Question 19

Provide an appropriate response.
-Consider the following figure, which is a square divided into two squares and two rectangles. 
 
The length of each side of the large square is $x + 8$. Use the formula for the area of a square to write the area of thi largest square as a power.

Accepted Answer

A)  $x ^ { 2 } - 8 ^ { 2 }$ 
B)  $x ^ { 2 } + 8 ^ { 2 }$ 
C)  $( x + 8 ) ^ { 2 }$ 
D)  $( x - 8 ) ^ { 2 }$ 
A)  $x ^ { 2 } - 8 ^ { 2 }$ 
B)  $x ^ { 2 } + 8 ^ { 2 }$ 
C)  $( x + 8 ) ^ { 2 }$ 
D)  $( x - 8 ) ^ { 2 }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 5 } { 4 } ( - 8 y )$$

Accepted Answer

A)  $20 \mathrm { y }$ 
B)  $- 10 y$ 
C)  $10 \mathrm { y }$ 
D)  $- 9 y$ 
A)  $20 \mathrm { y }$ 
B)  $- 10 y$ 
C)  $10 \mathrm { y }$ 
D)  $- 9 y$

Write in radical form. Assume all variables represent positive real numbers. - $2 x ^ { 1 / 3 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 9 + \frac { 3 } { s } } { \frac { s } { 4 } + \frac { 1 } { 12 } }$

Decide whether the expression has been simplified correctly. - $4 ^ { 0 } x = x$

Decide whether the expression has been simplified correctly. - $\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 6 }$

Find the domain of the expression. - $\frac { 2 x - 3 } { ( 4 x - 3 ) ( x + 6 ) }$

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

Find the sum or difference. - $( x + 4 ) ( - 3 x - 2 )$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 2,3,4,5,6,7,8,9,10,11,12 \} , \mathrm { M } = \{ 2,4,6,8 \} , \mathrm { N } = \{ 3,5,7,9,11 \} , \mathrm { Q } = \{ 2,4,6,8,10,12 \}$ , and $\mathrm { R } = \{ 2,3,4,5 \}$ . Q $\cap R ^ { \prime }$

Use set notation, and list all the elements of the set. -{19, 20, 21, . . . , 25}

Find the product or quotient. - $\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 14 k + 48 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 12 k + 35 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 5 r ^ { - 1 } \left( r ^ { 3 } \right) ^ { 4 } } { 2 \left( r ^ { - 2 } \right) ^ { - 2 } }$

Factor by any method. - $( 3 x - 2 ) ^ { 2 } - y ^ { 2 }$

Find the sum or difference. - $( n - 2 ) ( n - 2 ) ( n + 2 ) ( n + 2 )$

Find the product. Assume variables represent positive real numbers. - $y ^ { 1 / 3 } \left( y ^ { 4 / 9 } - 4 y ^ { 2 / 9 } \right)$

Factor by any method. - $( q - 4 ) ^ { 2 } - 9$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 12 } + \sqrt { 8 } ) ( \sqrt { 12 } - \sqrt { 8 } )$

Factor out the greatest common factor. Simplify the factors, if possible. - $5 t ^ { 2 } - 10 t - 25$

Find the product. Assume variables represent positive real numbers. - $- 9 k ^ { 1 / 8 } \left( 8 k ^ { 3 / 8 } - 5 k ^ { 3 / 4 } \right)$

Provide an appropriate response. -Consider the following figure, which is a square divided into two squares and two rectangles. The length of each side of the large square is $x + 8$ . Use the formula for the area of a square to write the area of thi largest square as a power.

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 5 } { 4 } ( - 8 y )$

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Exam 1: Review of Basic Concepts

Write in radical form. Assume all variables represent positive real numbers. - 2x1/32 x ^ { 1 / 3 }2x1/3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 9+3ss4+112\frac { 9 + \frac { 3 } { s } } { \frac { s } { 4 } + \frac { 1 } { 12 } }4s​+121​9+s3​​

Decide whether the expression has been simplified correctly. - 40x=x4 ^ { 0 } x = x40x=x

Decide whether the expression has been simplified correctly. - (x4)2=x6\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 6 }(x4)2=x6

Find the domain of the expression. - 2x−3(4x−3)(x+6)\frac { 2 x - 3 } { ( 4 x - 3 ) ( x + 6 ) }(4x−3)(x+6)2x−3​

Find the sum or difference. - 2x2(6x6+4x4)2 x ^ { 2 } \left( 6 x ^ { 6 } + 4 x ^ { 4 } \right)2x2(6x6+4x4)

Find the sum or difference. - (x+4)(−3x−2)( x + 4 ) ( - 3 x - 2 )(x+4)(−3x−2)