Question 1

Name the property illustrated by the statement.
-x + (y + z)= x + (z + y)

Accepted Answer

A) associative property of addition 
B) distributive property 
C) identity property of addition 
D) commutative property of addition 
A) associative property of addition 
B) distributive property 
C) identity property of addition 
D) commutative property of addition

Question 2

Express the value without exponents.
-$\left( 8 \times 10 ^ { 5 } \right) \times \left( 9 \times 10 ^ { 2 } \right)$

Accepted Answer

A) 7,200,000,000 
B) 72,000,000 
C) 720,000,000 
D) 72,000,000,000 
A) 7,200,000,000 
B) 72,000,000 
C) 720,000,000 
D) 72,000,000,000

Question 3

Evaluate the expression without using a calculator.
-$\sqrt [ 3 ] { \frac { 1 } { 216 } }$

Accepted Answer

A) 6 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 36 }$ 
D)  $\frac { 1 } { 216 }$ 
A) 6 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 36 }$ 
D)  $\frac { 1 } { 216 }$

Question 4

Evaluate the absolute value expression.
-$| - 4 |$

Accepted Answer

A) -4 
B) 0 
C) 8 
D) 4 
A) -4 
B) 0 
C) 8 
D) 4

Question 5

Evaluate the expression without using a calculator.
-$\sqrt [ 4 ] { \frac { 1 } { 16 } }$

Accepted Answer

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

Question 6

Evaluate the expression.
-$11 ( a + b ) ^ { 0 }$

Accepted Answer

A) 0 
B) 1 
C) 11a + 11b 
D) 11 
A) 0 
B) 1 
C) 11a + 11b 
D) 11

Question 7

Simplify the expression and write the answer without negative exponents.
-$\left( x ^ { - 7 } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 10 } }$ 
B)  $\frac { 1 } { x ^ { 21 } }$ 
C)  $- x ^ { 10 }$ 
D)  $x ^ { 21 }$ 
A)  $\frac { 1 } { x ^ { 10 } }$ 
B)  $\frac { 1 } { x ^ { 21 } }$ 
C)  $- x ^ { 10 }$ 
D)  $x ^ { 21 }$

Question 8

Simplify the expression and write the answer without negative exponents.
-$\frac { x ^ { 7 } } { x ^ { 6 } }$

Accepted Answer

A) x 
B)  $\frac { 1 } { x }$ 
C)  $x ^ { 13 }$ 
D)  $x ^ { 7 } - x ^ { 6 }$ 
A) x 
B)  $\frac { 1 } { x }$ 
C)  $x ^ { 13 }$ 
D)  $x ^ { 7 } - x ^ { 6 }$

Question 9

Evaluate.
-130 ÷ (-5)

Accepted Answer

A)  $- \frac { 1 } { 26 }$ 
B) -36 
C) -26 
D) 26 
A)  $- \frac { 1 } { 26 }$ 
B) -36 
C) -26 
D) 26

Question 10

Simplify the expression and write the answer without negative exponents.
-$\frac { \left( 3 x y ^ { 4 } z ^ { - 2 } \right) ^ { 3 } } { \left( 4 x ^ { 6 } y z ^ { - 3 } \right) ^ { - 1 } }$

Accepted Answer

A)  $- \frac { 27 y ^ { 13 } } { 4 x ^ { 3 } z ^ { 9 } }$ 
B)  $\frac { 108 y ^ { 13 } } { x ^ { 5 } z ^ { 9 } }$ 
C)  $- \frac { 27 x ^ { 9 } y ^ { 13 } } { 4 z ^ { 9 } }$ 
D)  $\frac { 108 x ^ { 9 } y ^ { 13 } } { z ^ { 9 } }$ 
A)  $- \frac { 27 y ^ { 13 } } { 4 x ^ { 3 } z ^ { 9 } }$ 
B)  $\frac { 108 y ^ { 13 } } { x ^ { 5 } z ^ { 9 } }$ 
C)  $- \frac { 27 x ^ { 9 } y ^ { 13 } } { 4 z ^ { 9 } }$ 
D)  $\frac { 108 x ^ { 9 } y ^ { 13 } } { z ^ { 9 } }$

Question 11

Evaluate the expression.
-$\left( \frac { 2 } { 3 } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { 27 } { 8 }$ 
B)  $\frac { 8 } { 27 }$ 
C)  $- \frac { 27 } { 8 }$ 
D)  $- \frac { 8 } { 27 }$ 
A)  $\frac { 27 } { 8 }$ 
B)  $\frac { 8 } { 27 }$ 
C)  $- \frac { 27 } { 8 }$ 
D)  $- \frac { 8 } { 27 }$

Question 12

Determine whether the statement is true or false.
-The intersection of the set of rational numbers with the set of irrational numbers is the empty set.

Accepted Answer

A) True 
 B)False

Question 13

Evaluate the expression.
-$4 ( x y z ) ^ { 0 }$

Accepted Answer

A) 4xyz 
B) 4 
C) 0 
D) xyz 
A) 4xyz 
B) 4 
C) 0 
D) xyz

Question 14

$\mathbf { Find~ A \cup R ~and A \cap R~ for~ the~ sets~ A~ and~ B}$
-A = { $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}$ B = { $\left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\}$

Accepted Answer

A)  $\begin{array} { l } 
A \cup B = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } \right\} \\
A \cap B = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}
\end{array}$ 
B)  $\begin{array} { l } 
\mathrm { A } \cup \mathrm { B } = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\} \\
\mathrm { A } \cap \mathrm { B } = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}
\end{array}$ 
C)  $\begin{array} { l } 
\mathrm { A } \cup \mathrm { B } = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\} \\
\mathrm { A } \cap \mathrm { B } = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\}
\end{array}$ 
D)  $\begin{array} { l } 
A \cup B = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\} \\
A \cap B = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } \right\}
\end{array}$ 
A)  $\begin{array} { l } 
A \cup B = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } \right\} \\
A \cap B = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}
\end{array}$ 
B)  $\begin{array} { l } 
\mathrm { A } \cup \mathrm { B } = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\} \\
\mathrm { A } \cap \mathrm { B } = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}
\end{array}$ 
C)  $\begin{array} { l } 
\mathrm { A } \cup \mathrm { B } = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\} \\
\mathrm { A } \cap \mathrm { B } = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\}
\end{array}$ 
D)  $\begin{array} { l } 
A \cup B = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\} \\
A \cap B = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } \right\}
\end{array}$

Question 15

Determine whether the statement is true or false.
-Some real numbers are integers.

Accepted Answer

A) True 
 B)False

Question 16

Solve. Express the result in scientific notation. Round to the nearest hundredth, if necessary.
-The mass of a neutron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of 424,000,000 neutrons.

Accepted Answer

A)  $3.86 \times 10 ^ { - 18 } \text { grams }$ 
B)  $3.86 \times 10 ^ { - 20 } \text { grams }$ 
C)  $3.86 \times 10 ^ { - 17 } \text { grams }$ 
D)  $3.86 \times 10 ^ { - 19 } \text { grams }$ 
A)  $3.86 \times 10 ^ { - 18 } \text { grams }$ 
B)  $3.86 \times 10 ^ { - 20 } \text { grams }$ 
C)  $3.86 \times 10 ^ { - 17 } \text { grams }$ 
D)  $3.86 \times 10 ^ { - 19 } \text { grams }$

Question 17

$\mathbf { Evaluate ~i)~ x ^ { 2 }~  and~ ii) - x ^ { 2 } ~ for~ the~ given~ value ~of  ~x . }$
-$\frac { 1 } { 8 }$

Accepted Answer

A)  i) $\frac { 1 } { 64 }$
ii) $- \frac { 1 } { 64 }$ 
B)  i) $\frac { 1 } { 64 }$

ii) $\frac { 1 } { 64 }$ 
C)  i) $- \frac { 1 } { 64 }$
ii) $\frac { 1 } { 64 }$ 
D)  i) 64
ii) $- 64$ 
A)  i) $\frac { 1 } { 64 }$
ii) $- \frac { 1 } { 64 }$ 
B)  i) $\frac { 1 } { 64 }$

ii) $\frac { 1 } { 64 }$ 
C)  i) $- \frac { 1 } { 64 }$
ii) $\frac { 1 } { 64 }$ 
D)  i) 64
ii) $- 64$

Question 18

Evaluate the expression for the given value or values.
-$3 x ^ { 2 } + 2 x + 2 \text { when } x = 3$

Accepted Answer

A) 23 
B) 31 
C) 35 
D) 27 
A) 23 
B) 31 
C) 35 
D) 27

Question 19

Evaluate.
--2(0)

Accepted Answer

A) 0 
B) 2 
C) -4 
D) -2 
A) 0 
B) 2 
C) -4 
D) -2

Question 20

$$\mathbf { Insert  , or =  in~ the ~blank~ to~ make ~the ~statement~ true. }$$
-$- | - 4 |$_________$|-10|$

Accepted Answer

A)   
A)

Name the property illustrated by the statement. -x + (y + z)= x + (z + y)

Express the value without exponents. - $\left( 8 \times 10 ^ { 5 } \right) \times \left( 9 \times 10 ^ { 2 } \right)$

Evaluate the expression without using a calculator. - $\sqrt [ 3 ] { \frac { 1 } { 216 } }$

Evaluate the absolute value expression. - $| - 4 |$

Evaluate the expression without using a calculator. - $\sqrt [ 4 ] { \frac { 1 } { 16 } }$

Evaluate the expression. - $11 ( a + b ) ^ { 0 }$

Simplify the expression and write the answer without negative exponents. - $\left( x ^ { - 7 } \right) ^ { - 3 }$

Simplify the expression and write the answer without negative exponents. - $\frac { x ^ { 7 } } { x ^ { 6 } }$

Evaluate. -130 ÷ (-5)

Simplify the expression and write the answer without negative exponents. - $\frac { \left( 3 x y ^ { 4 } z ^ { - 2 } \right) ^ { 3 } } { \left( 4 x ^ { 6 } y z ^ { - 3 } \right) ^ { - 1 } }$

Evaluate the expression. - $\left( \frac { 2 } { 3 } \right) ^ { - 3 }$

Determine whether the statement is true or false. -The intersection of the set of rational numbers with the set of irrational numbers is the empty set.

Evaluate the expression. - $4 ( x y z ) ^ { 0 }$

$\mathbf { Find~ A \cup R ~and A \cap R~ for~ the~ sets~ A~ and~ B}$ -A = { $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}$ B = { $\left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\}$

Determine whether the statement is true or false. -Some real numbers are integers.

Solve. Express the result in scientific notation. Round to the nearest hundredth, if necessary. -The mass of a neutron is approximately $9.11 \times 10 ^ { - 28 }$ grams. Find the mass of 424,000,000 neutrons.

$\mathbf { Evaluate ~i)~ x ^ { 2 }~ and~ ii) - x ^ { 2 } ~ for~ the~ given~ value ~of ~x . }$ - $\frac { 1 } { 8 }$

Evaluate the expression for the given value or values. - $3 x ^ { 2 } + 2 x + 2 \text { when } x = 3$

Evaluate. --2(0)

$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$ - $- | - 4 |$ _________ $|-10|$

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Exam 1: Basic Concepts

Name the property illustrated by the statement. -x + (y + z)= x + (z + y)

Express the value without exponents. - (8×105)×(9×102)\left( 8 \times 10 ^ { 5 } \right) \times \left( 9 \times 10 ^ { 2 } \right)(8×105)×(9×102)

Evaluate the expression without using a calculator. - 12163\sqrt [ 3 ] { \frac { 1 } { 216 } }32161​​

Evaluate the absolute value expression. - ∣−4∣| - 4 |∣−4∣

Evaluate the expression without using a calculator. - 1164\sqrt [ 4 ] { \frac { 1 } { 16 } }4161​​

Evaluate the expression. - 11(a+b)011 ( a + b ) ^ { 0 }11(a+b)0

Simplify the expression and write the answer without negative exponents. - (x−7)−3\left( x ^ { - 7 } \right) ^ { - 3 }(x−7)−3

Simplify the expression and write the answer without negative exponents. - x7x6\frac { x ^ { 7 } } { x ^ { 6 } }x6x7​