Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { 5 } { 9 x ^ { 2 } } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 15 x } } { 3 x }$ 
B)  $\frac { \sqrt [ 3 ] { 405 x ^ { 2 } } } { 9 x }$ 
C)  $\frac { \sqrt [ 3 ] { 405 x } } { 81 }$ 
D)  $\frac { \sqrt [ 3 ] { 45 x } } { 9 x }$ 
A)  $\frac { \sqrt [ 3 ] { 15 x } } { 3 x }$ 
B)  $\frac { \sqrt [ 3 ] { 405 x ^ { 2 } } } { 9 x }$ 
C)  $\frac { \sqrt [ 3 ] { 405 x } } { 81 }$ 
D)  $\frac { \sqrt [ 3 ] { 45 x } } { 9 x }$

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 8 x ^ { 2 } y } { 25 } }$$

Accepted Answer

A)  $4 x \sqrt { 2 y }$ 
B)  $\frac { 2 \sqrt { 2 x ^ { 2 } y } } { 5 }$ 
C)  $\frac { 2 x \sqrt { 2 y } } { 5 }$ 
D)  $x \sqrt { \frac { 8 y } { 5 } }$ 
A)  $4 x \sqrt { 2 y }$ 
B)  $\frac { 2 \sqrt { 2 x ^ { 2 } y } } { 5 }$ 
C)  $\frac { 2 x \sqrt { 2 y } } { 5 }$ 
D)  $x \sqrt { \frac { 8 y } { 5 } }$

Question 3

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

Accepted Answer

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

Question 4

Provide an appropriate response.
-The number of farms in a certain country since 1940 , in millions, can be approximated by evaluating the polynomial $0.000026045689 \mathrm { x } ^ { 3 } - 0.1522580959 \mathrm { x } ^ { 2 } + 296.5669762 \mathrm { x } - 192,464.713$, where $\mathrm { x }$ is the year in question. Evaluate the polynomial for $x = 1970$ to determine the number of farms in 1970 . Round the answer to the nearest million farms.

Accepted Answer

A)  5 million farms 
B)  3 million farms 
C)  6 million farms 
D)  2 million farms 
A)  5 million farms 
B)  3 million farms 
C)  6 million farms 
D)  2 million farms

Question 5

Evaluate the expression.
-$$- \left| \frac { 1 } { 7 } \right|$$

Accepted Answer

A)  0 
B)  $- \frac { 1 } { 7 }$ 
C)  $\pm \frac { 1 } { 7 }$ 
D)  $\frac { 1 } { 7 }$ 
A)  0 
B)  $- \frac { 1 } { 7 }$ 
C)  $\pm \frac { 1 } { 7 }$ 
D)  $\frac { 1 } { 7 }$

Question 6

Write in radical form. Assume all variables represent positive real numbers.
-$x ^ { 1 / 8 }$

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 8 ] { x } }$ 
B)  $\sqrt { x ^ { 8 } }$ 
C)  $\sqrt [ 8 ] { x }$ 
D)  $x ^ { - 8 }$ 
A)  $\frac { 1 } { \sqrt [ 8 ] { x } }$ 
B)  $\sqrt { x ^ { 8 } }$ 
C)  $\sqrt [ 8 ] { x }$ 
D)  $x ^ { - 8 }$

Question 7

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 7,8,9,10,11,12,13,14,15,16,17 \} , \mathrm { M } = \{ 7,9,11,13 \} , \mathrm { N } = \{ 8,10,12,14,16 \} , \mathrm { Q } = \{ 7,9,11,13,15,17 \}$, and $\mathrm { R } = \{ 7,8,9,10 \}$.
$( \mathrm { U } \cup \emptyset ) \cap \mathrm { R } ^ { \prime }$

Accepted Answer

A)  $\mathrm { U }$, or $\{ 7,8,9,10,11,12,13,14,15,16,17 \}$ 
B)  $\varnothing$; R' and (U $\cup \varnothing )$ are disjoint sets. 
C)  $R$, or $\{ 7,8,9,10 \}$ 
D)  $\{ 11,12,13,14,15,16,17 \}$ 
A)  $\mathrm { U }$, or $\{ 7,8,9,10,11,12,13,14,15,16,17 \}$ 
B)  $\varnothing$; R' and (U $\cup \varnothing )$ are disjoint sets. 
C)  $R$, or $\{ 7,8,9,10 \}$ 
D)  $\{ 11,12,13,14,15,16,17 \}$

Question 8

Simplify the expression. Assume all variables represent positive real numbers.
-$2 \sqrt { 3 } - 9 \sqrt { 27 }$

Accepted Answer

A)  $- 29 \sqrt { 3 }$ 
B)  $25 \sqrt { 3 }$ 
C)  $- 7 \sqrt { 3 }$ 
D)  $- 25 \sqrt { 3 }$ 
A)  $- 29 \sqrt { 3 }$ 
B)  $25 \sqrt { 3 }$ 
C)  $- 7 \sqrt { 3 }$ 
D)  $- 25 \sqrt { 3 }$

Question 9

Determine the degree of the polynomial.
-$- 3 a ^ { 4 } - 16 a ^ { 2 } + 8 a + 4 a ^ { 6 }$

Accepted Answer

A)  12 
B)  6 
C)  4 
D)  13 
A)  12 
B)  6 
C)  4 
D)  13

Question 10

Insert   in the blank to make the statement true.
-

Accepted Answer

A)  $\subseteq$ 
B)  $\not$ 
A)  $\subseteq$ 
B)  $\not$

Question 11

Identify the set as finite or infinite.
-$\{ x \mid x \text { is a fraction between } 0 \text { and } 1 \}$

Accepted Answer

A)  finite 
B)  infinite 
A)  finite 
B)  infinite

Question 12

Factor the trinomial, if possible.
-$( m + 2 n ) ^ { 2 } - 4 ( m + 2 n ) + 4$

Accepted Answer

A)  $( m + 2 n + 2 ) ^ { 2 }$ 
B)  $( m + 2 n - 2 ) ^ { 2 }$ 
C)  $( m - n - 4 ) ^ { 2 }$ 
D)  $( m - 2 n - 2 ) ^ { 2 }$ 
A)  $( m + 2 n + 2 ) ^ { 2 }$ 
B)  $( m + 2 n - 2 ) ^ { 2 }$ 
C)  $( m - n - 4 ) ^ { 2 }$ 
D)  $( m - 2 n - 2 ) ^ { 2 }$

Question 13

Find the sum or difference.
-$$2 \left( - 2 r ^ { 4 } + 9 r ^ { 3 } - 3 r \right) - 3 \left( 8 r ^ { 4 } - 9 r ^ { 3 } + 6 r ^ { 2 } - 2 r \right)$$

Accepted Answer

A)  $- 28 r ^ { 4 } + 45 r ^ { 3 } - 18 r ^ { 2 }$ 
B)  $- 28 r ^ { 4 } - 9 r ^ { 3 } + 18 r ^ { 2 } - 12 r$ 
C)  $- 28 r ^ { 4 } + 18 r ^ { 3 } - 6 r ^ { 2 } - r$ 
D)  $- 28 r ^ { 4 } + 6 r ^ { 2 } - 5 r$ 
A)  $- 28 r ^ { 4 } + 45 r ^ { 3 } - 18 r ^ { 2 }$ 
B)  $- 28 r ^ { 4 } - 9 r ^ { 3 } + 18 r ^ { 2 } - 12 r$ 
C)  $- 28 r ^ { 4 } + 18 r ^ { 3 } - 6 r ^ { 2 } - r$ 
D)  $- 28 r ^ { 4 } + 6 r ^ { 2 } - 5 r$

Question 14

Find the product. Assume variables represent positive real numbers.
-$7 x ^ { 7 / 5 } \left( x ^ { 11 / 5 } - 6 x \right)$

Accepted Answer

A)  $7 x ^ { 18 / 5 } - \frac { 42 } { x ^ { 12 / 5 } }$ 
B)  $\frac{7}{x^{18 / 5}}-42 x^{12 / 5}$ 
C)  $\frac { 7 } { x ^ { 18 / 5 } } - \frac { 42 } { x ^ { 12 / 5 } }$ 
D)  $7 x ^ { 18 / 5 } - 42 x ^ { 12 / 5 }$ 
A)  $7 x ^ { 18 / 5 } - \frac { 42 } { x ^ { 12 / 5 } }$ 
B)  $\frac{7}{x^{18 / 5}}-42 x^{12 / 5}$ 
C)  $\frac { 7 } { x ^ { 18 / 5 } } - \frac { 42 } { x ^ { 12 / 5 } }$ 
D)  $7 x ^ { 18 / 5 } - 42 x ^ { 12 / 5 }$

Question 15

Tell whether the statement is true or false.
-$$6 \in \{ 4,54,6,7 \}$$

Accepted Answer

A) True 
 B)False

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 245 x ^ { 2 } }$

Accepted Answer

A)  $245 x$ 
B)  $7 \times \sqrt { 5 }$ 
C)  $5 x ^ { 2 } \sqrt { 7 }$ 
D)  $7 \sqrt { 5 x }$ 
A)  $245 x$ 
B)  $7 \times \sqrt { 5 }$ 
C)  $5 x ^ { 2 } \sqrt { 7 }$ 
D)  $7 \sqrt { 5 x }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$( 2 \sqrt { 7 } + 10 \sqrt { 5 } ) ( 2 \sqrt { 7 } + 6 \sqrt { 5 } )$

Accepted Answer

A)  $4 \sqrt { 7 } + 60 \sqrt { 5 }$ 
B)  $- 272 + 32 \sqrt { 35 }$ 
C)  $328 + 32 \sqrt { 35 }$ 
D)  $4 \sqrt { 7 } + 60 \sqrt { 5 } + 32 \sqrt { 35 }$ 
A)  $4 \sqrt { 7 } + 60 \sqrt { 5 }$ 
B)  $- 272 + 32 \sqrt { 35 }$ 
C)  $328 + 32 \sqrt { 35 }$ 
D)  $4 \sqrt { 7 } + 60 \sqrt { 5 } + 32 \sqrt { 35 }$

Question 18

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$( - 2 x ) ^ { 0 }$

Accepted Answer

A)  0 
B)  1 
C)  $- 1$ 
D)  2 
A)  0 
B)  1 
C)  $- 1$ 
D)  2

Question 19

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true.
-

Accepted Answer

A)  $\in$ 
B)  $\notin$ 
A)  $\in$ 
B)  $\notin$

Question 20

Identify the expression as a polynomial or not a polynomial.
-$2 x - \frac { 9 } { x } + 4$

Accepted Answer

A)  Polynomial 
B)  Not a polynomial 
A)  Polynomial 
B)  Not a polynomial

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 5 } { 9 x ^ { 2 } } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 8 x ^ { 2 } y } { 25 } }$

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

Evaluate the expression. - $- \left| \frac { 1 } { 7 } \right|$

Write in radical form. Assume all variables represent positive real numbers. - $x ^ { 1 / 8 }$

Simplify the expression. Assume all variables represent positive real numbers. - $2 \sqrt { 3 } - 9 \sqrt { 27 }$

Determine the degree of the polynomial. - $- 3 a ^ { 4 } - 16 a ^ { 2 } + 8 a + 4 a ^ { 6 }$

Insert in the blank to make the statement true. -

Identify the set as finite or infinite. - $\{ x \mid x \text { is a fraction between } 0 \text { and } 1 \}$

Factor the trinomial, if possible. - $( m + 2 n ) ^ { 2 } - 4 ( m + 2 n ) + 4$

Find the sum or difference. - $2 \left( - 2 r ^ { 4 } + 9 r ^ { 3 } - 3 r \right) - 3 \left( 8 r ^ { 4 } - 9 r ^ { 3 } + 6 r ^ { 2 } - 2 r \right)$

Find the product. Assume variables represent positive real numbers. - $7 x ^ { 7 / 5 } \left( x ^ { 11 / 5 } - 6 x \right)$

Tell whether the statement is true or false. - $6 \in \{ 4,54,6,7 \}$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 245 x ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $( 2 \sqrt { 7 } + 10 \sqrt { 5 } ) ( 2 \sqrt { 7 } + 6 \sqrt { 5 } )$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 2 x ) ^ { 0 }$

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. - $Insert \in \mathbf { O r } \notin in the blank to make the statement is true. -$

Identify the expression as a polynomial or not a polynomial. - $2 x - \frac { 9 } { x } + 4$

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Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 59x23\sqrt [ 3 ] { \frac { 5 } { 9 x ^ { 2 } } }39x25​​

Simplify the expression. Assume all variables represent positive real numbers. - 8x2y25\sqrt { \frac { 8 x ^ { 2 } y } { 25 } }258x2y​​

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​

Evaluate the expression. - −∣17∣- \left| \frac { 1 } { 7 } \right|−​71​​

Write in radical form. Assume all variables represent positive real numbers. - x1/8x ^ { 1 / 8 }x1/8

Simplify the expression. Assume all variables represent positive real numbers. - 23−9272 \sqrt { 3 } - 9 \sqrt { 27 }23​−927​

Determine the degree of the polynomial. - −3a4−16a2+8a+4a6- 3 a ^ { 4 } - 16 a ^ { 2 } + 8 a + 4 a ^ { 6 }−3a4−16a2+8a+4a6