Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 49 } { 2 } }$

Accepted Answer

A)  $\frac { 7 \sqrt { 2 } } { 2 }$ 
B)  11 
C)  $\frac { 49 \sqrt { 2 } } { 2 }$ 
D)  $7 \sqrt { 2 }$ 
A)  $\frac { 7 \sqrt { 2 } } { 2 }$ 
B)  11 
C)  $\frac { 49 \sqrt { 2 } } { 2 }$ 
D)  $7 \sqrt { 2 }$

Question 2

Factor the trinomial, if possible.
-$36 m ^ { 2 } + 72 m + 36$

Accepted Answer

A)  $( 6 m - 7 ) ^ { 2 }$ 
B)  $36 ( m - 1 ) ^ { 2 }$ 
C)  $36 ( m + 1 ) ^ { 2 }$ 
D)  $( 6 m + 7 ) ^ { 2 }$ 
A)  $( 6 m - 7 ) ^ { 2 }$ 
B)  $36 ( m - 1 ) ^ { 2 }$ 
C)  $36 ( m + 1 ) ^ { 2 }$ 
D)  $( 6 m + 7 ) ^ { 2 }$

Question 3

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\frac { x ^ { 1 / 2 } } { x ^ { 5 / 4 } \cdot x ^ { - 2 } }$

Accepted Answer

A)  $x ^ { 15 / 4 }$ 
B)  $x ^ { 5 / 4 }$ 
C)  $\frac { 1 } { x ^ { 5 / 4 } }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 15 / 4 } }$ 
A)  $x ^ { 15 / 4 }$ 
B)  $x ^ { 5 / 4 }$ 
C)  $\frac { 1 } { x ^ { 5 / 4 } }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 15 / 4 } }$

Question 4

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { x ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 16 } y ^ { 8 } }$$

Accepted Answer

A)  $x ^ { 5 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
B)  $x ^ { 5 } y ^ { 5 } \sqrt [ 3 ] { x y }$ 
C)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
D)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x ^ { 2 } y }$ 
A)  $x ^ { 5 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
B)  $x ^ { 5 } y ^ { 5 } \sqrt [ 3 ] { x y }$ 
C)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
D)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x ^ { 2 } y }$

Question 5

Evaluate the expression.
-$$\left( 9 - 8 ^ { 2 } \right) ( - 8 + \sqrt { 81 } )$$

Accepted Answer

A)  $- 4895$ 
B)  $- 47$ 
C)  $- 55$ 
D)  73 
A)  $- 4895$ 
B)  $- 47$ 
C)  $- 55$ 
D)  73

Question 6

Factor the polynomial by substitution.
-$$a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }$$

Accepted Answer

A)  $( a + b ) ^ { 2 } ( a - 9 b ) ( a + 8 b )$ 
B)  $( a - 9 b ) ( a + 8 b ) ( a + b )$ 
C)  $( a + b ) ^ { 2 } ( a - 8 b ) ( a + 9 b )$ 
D)  $( a + b ) ^ { 2 } ( a - 9 ) ( a + 8 )$ 
A)  $( a + b ) ^ { 2 } ( a - 9 b ) ( a + 8 b )$ 
B)  $( a - 9 b ) ( a + 8 b ) ( a + b )$ 
C)  $( a + b ) ^ { 2 } ( a - 8 b ) ( a + 9 b )$ 
D)  $( a + b ) ^ { 2 } ( a - 9 ) ( a + 8 )$

Question 7

Find the sum or difference.
-$$( 12 p + 13 ) ( 12 p - 13 )$$

Accepted Answer

A)  $144 p ^ { 2 } - 169$ 
B)  $p ^ { 2 } - 169$ 
C)  $144 p ^ { 2 } + 312 p - 169$ 
D)  $144 p ^ { 2 } - 312 p - 169$ 
A)  $144 p ^ { 2 } - 169$ 
B)  $p ^ { 2 } - 169$ 
C)  $144 p ^ { 2 } + 312 p - 169$ 
D)  $144 p ^ { 2 } - 312 p - 169$

Question 8

Factor the trinomial, if possible.
-4x $$x ^ { 3 } + 4 x ^ { 2 } y - 24 x y ^ { 2 }$$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 8 x y \right) ( x - 3 y )$ 
B)  $( x - 2 y ) \left( 4 x ^ { 2 } + 12 x y \right)$ 
C)  $4 x ( x - 2 y ) ( x + 3 y )$ 
D)  $4 x ( x + 2 y ) ( x - 3 y )$ 
A)  $\left( 4 x ^ { 2 } + 8 x y \right) ( x - 3 y )$ 
B)  $( x - 2 y ) \left( 4 x ^ { 2 } + 12 x y \right)$ 
C)  $4 x ( x - 2 y ) ( x + 3 y )$ 
D)  $4 x ( x + 2 y ) ( x - 3 y )$

Question 9

Factor the trinomial, if possible.
-$$x ^ { 2 } + 2 x y - 8 y ^ { 2 }$$

Accepted Answer

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

Question 10

Factor out the greatest common factor. Simplify the factors, if possible.
-$$\mathrm { t } ( 4 - \mathrm { m } ) + \mathrm { s } ( 4 - \mathrm { m } )$$

Accepted Answer

A)  $( t - s ) ( 4 - m )$ 
B)  $( t + s ) ( 4 + m )$ 
C)  $( \mathrm { t } + \mathrm { s } ) ( 4 - \mathrm { m } )$ 
D)  $\mathrm { t } ( 4 - \mathrm { m } ) + \mathrm { s }$ 
A)  $( t - s ) ( 4 - m )$ 
B)  $( t + s ) ( 4 + m )$ 
C)  $( \mathrm { t } + \mathrm { s } ) ( 4 - \mathrm { m } )$ 
D)  $\mathrm { t } ( 4 - \mathrm { m } ) + \mathrm { s }$

Question 11

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 4,5,6,7,8,9,10,11,12,13,14 \} , \mathrm { M } = \{ 4,6,8,10 \} , \mathrm { N } = \{ 5,7,9,11,13 \} , \mathrm { Q } = \{ 4,6,8,10,12,14 \}$, and $\mathrm { R } = \{ 4,5,6,7 \}$.
$\mathrm { M } \cup \mathrm { N }$

Accepted Answer

A)  $\{ 5,6,7,8,9,10,11,12,13 \}$ 
B)  $\{ 4,5,6,7,8,9,13 \}$ 
C)  $\varnothing ; \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
D)  $\{ 4,5,6,7,8,9,10,11,13 \}$ 
A)  $\{ 5,6,7,8,9,10,11,12,13 \}$ 
B)  $\{ 4,5,6,7,8,9,13 \}$ 
C)  $\varnothing ; \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
D)  $\{ 4,5,6,7,8,9,10,11,13 \}$

Question 12

Evaluate the expression.
-$- 3^6$

Accepted Answer

A)  18 
B)  729 
C)  $- 729$ 
D)  $- 18$ 
A)  18 
B)  729 
C)  $- 729$ 
D)  $- 18$

Question 13

Find the sum or difference.
-$( x + 4 ) ( 5 x - 5 )$

Accepted Answer

A)  $5 x ^ { 2 } + 13 x - 20$ 
B)  $5 x ^ { 2 } - 20 x + 15$ 
C)  $5 x ^ { 2 } + 15 x - 20$ 
D)  $5 x ^ { 2 } + 15 x + 15$ 
A)  $5 x ^ { 2 } + 13 x - 20$ 
B)  $5 x ^ { 2 } - 20 x + 15$ 
C)  $5 x ^ { 2 } + 15 x - 20$ 
D)  $5 x ^ { 2 } + 15 x + 15$

Question 14

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { - 8 } y ^ { 9 } } { x ^ { - 2 } y ^ { 7 } }$$

Accepted Answer

A)  $\frac { y ^ { 3 } } { x ^ { 7 } }$ 
B)  $\frac { x ^ { 6 } } { y ^ { 2 } }$ 
C)  $\frac { y ^ { 2 } } { x ^ { 6 } }$ 
D)  $\frac { x ^ { 7 } } { y ^ { 3 } }$ 
A)  $\frac { y ^ { 3 } } { x ^ { 7 } }$ 
B)  $\frac { x ^ { 6 } } { y ^ { 2 } }$ 
C)  $\frac { y ^ { 2 } } { x ^ { 6 } }$ 
D)  $\frac { x ^ { 7 } } { y ^ { 3 } }$

Question 15

Find the sum or difference.
-$$( 2 x - 6 ) ( x + 5 )$$

Accepted Answer

A)  $2 x ^ { 2 } + 4 x - 30$ 
B)  $x ^ { 2 } - 30 x + 4$ 
C)  $x ^ { 2 } + 4 x + 3$ 
D)  $2 x ^ { 2 } + 3 x - 30$ 
A)  $2 x ^ { 2 } + 4 x - 30$ 
B)  $x ^ { 2 } - 30 x + 4$ 
C)  $x ^ { 2 } + 4 x + 3$ 
D)  $2 x ^ { 2 } + 3 x - 30$

Question 16

Write in radical form. Assume all variables represent positive real numbers.
-$( 7 x ) ^ { 1 / 3 }$

Accepted Answer

A)  $\sqrt [ 3 ] { 7 x }$ 
B)  $\sqrt [ 1 / 3 ] { 7 x }$ 
C)  $\frac { 1 } { \sqrt [ 3 ] { 7 x } }$ 
D)  $\frac { \sqrt { 7 x } } { 3 }$ 
A)  $\sqrt [ 3 ] { 7 x }$ 
B)  $\sqrt [ 1 / 3 ] { 7 x }$ 
C)  $\frac { 1 } { \sqrt [ 3 ] { 7 x } }$ 
D)  $\frac { \sqrt { 7 x } } { 3 }$

Question 17

Find the product or quotient.
-$$\frac { 5 p - 5 } { p } \cdot \frac { 6 p ^ { 2 } } { 4 p - 4 }$$

Accepted Answer

A)  $\frac { 2 } { 15 } p$ 
B)  $\frac { 30 p ^ { 3 } - 30 p ^ { 2 } } { 4 p ^ { 2 } - 4 p }$ 
C)  $\frac { 20 p ^ { 2 } + 40 p + 20 } { 6 p ^ { 3 } }$ 
D)  $\frac { 15 } { 2 } p$ 
A)  $\frac { 2 } { 15 } p$ 
B)  $\frac { 30 p ^ { 3 } - 30 p ^ { 2 } } { 4 p ^ { 2 } - 4 p }$ 
C)  $\frac { 20 p ^ { 2 } + 40 p + 20 } { 6 p ^ { 3 } }$ 
D)  $\frac { 15 } { 2 } p$

Question 18

Evaluate the expression.
-$$400 ^ { 1 / 2 }$$

Accepted Answer

A)  80 
B)  10 
C)  20 
D)  40 
A)  80 
B)  10 
C)  20 
D)  40

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - \frac { 216 } { 125 } }$$

Accepted Answer

A)  $\frac { 6 } { 5 }$ 
B)  $\frac { 36 } { 25 }$ 
C)  $- \frac { 216 } { 125 }$ 
D)  $- \frac { 6 } { 5 }$ 
A)  $\frac { 6 } { 5 }$ 
B)  $\frac { 36 } { 25 }$ 
C)  $- \frac { 216 } { 125 }$ 
D)  $- \frac { 6 } { 5 }$

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 15 } \cdot \sqrt { 48 }$

Accepted Answer

A)  $20 \sqrt { 3 }$ 
B)  $12 \sqrt { 5 }$ 
C)  $- 20 \sqrt { 3 }$ 
D)  $- 12 \sqrt { 5 }$ 
A)  $20 \sqrt { 3 }$ 
B)  $12 \sqrt { 5 }$ 
C)  $- 20 \sqrt { 3 }$ 
D)  $- 12 \sqrt { 5 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 49 } { 2 } }$

Factor the trinomial, if possible. - $36 m ^ { 2 } + 72 m + 36$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 1 / 2 } } { x ^ { 5 / 4 } \cdot x ^ { - 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { x ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 16 } y ^ { 8 } }$

Evaluate the expression. - $\left( 9 - 8 ^ { 2 } \right) ( - 8 + \sqrt { 81 } )$

Factor the polynomial by substitution. - $a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }$

Find the sum or difference. - $( 12 p + 13 ) ( 12 p - 13 )$

Factor the trinomial, if possible. -4x $x ^ { 3 } + 4 x ^ { 2 } y - 24 x y ^ { 2 }$

Factor the trinomial, if possible. - $x ^ { 2 } + 2 x y - 8 y ^ { 2 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $\mathrm { t } ( 4 - \mathrm { m } ) + \mathrm { s } ( 4 - \mathrm { m } )$

Evaluate the expression. - $- 3^6$

Find the sum or difference. - $( x + 4 ) ( 5 x - 5 )$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 8 } y ^ { 9 } } { x ^ { - 2 } y ^ { 7 } }$

Find the sum or difference. - $( 2 x - 6 ) ( x + 5 )$

Write in radical form. Assume all variables represent positive real numbers. - $( 7 x ) ^ { 1 / 3 }$

Find the product or quotient. - $\frac { 5 p - 5 } { p } \cdot \frac { 6 p ^ { 2 } } { 4 p - 4 }$

Evaluate the expression. - $400 ^ { 1 / 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - \frac { 216 } { 125 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 15 } \cdot \sqrt { 48 }$

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Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 492\sqrt { \frac { 49 } { 2 } }249​​

Factor the trinomial, if possible. - 36m2+72m+3636 m ^ { 2 } + 72 m + 3636m2+72m+36

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x1/2x5/4⋅x−2\frac { x ^ { 1 / 2 } } { x ^ { 5 / 4 } \cdot x ^ { - 2 } }x5/4⋅x−2x1/2​

Simplify the expression. Assume all variables represent positive real numbers. - x53⋅x16y83\sqrt [ 3 ] { x ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 16 } y ^ { 8 } }3x5​⋅3x16y8​

Evaluate the expression. - (9−82)(−8+81)\left( 9 - 8 ^ { 2 } \right) ( - 8 + \sqrt { 81 } )(9−82)(−8+81​)

Factor the polynomial by substitution. - a2(a+b)2−ab(a+b)2−72b2(a+b)2a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }a2(a+b)2−ab(a+b)2−72b2(a+b)2

Find the sum or difference. - (12p+13)(12p−13)( 12 p + 13 ) ( 12 p - 13 )(12p+13)(12p−13)

Factor the trinomial, if possible. -4x x3+4x2y−24xy2x ^ { 3 } + 4 x ^ { 2 } y - 24 x y ^ { 2 }x3+4x2y−24xy2

Factor the trinomial, if possible. - x2+2xy−8y2x ^ { 2 } + 2 x y - 8 y ^ { 2 }x2+2xy−8y2

Factor out the greatest common factor. Simplify the factors, if possible. - t(4−m)+s(4−m)\mathrm { t } ( 4 - \mathrm { m } ) + \mathrm { s } ( 4 - \mathrm { m } )t(4−m)+s(4−m)

Evaluate the expression. - −36- 3^6−36

Find the sum or difference. - (x+4)(5x−5)( x + 4 ) ( 5 x - 5 )(x+4)(5x−5)

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x−8y9x−2y7\frac { x ^ { - 8 } y ^ { 9 } } { x ^ { - 2 } y ^ { 7 } }x−2y7x−8y9​

Find the sum or difference. - (2x−6)(x+5)( 2 x - 6 ) ( x + 5 )(2x−6)(x+5)

Write in radical form. Assume all variables represent positive real numbers. - (7x)1/3( 7 x ) ^ { 1 / 3 }(7x)1/3

Find the product or quotient. - 5p−5p⋅6p24p−4\frac { 5 p - 5 } { p } \cdot \frac { 6 p ^ { 2 } } { 4 p - 4 }p5p−5​⋅4p−46p2​

Evaluate the expression. - 4001/2400 ^ { 1 / 2 }4001/2

Simplify the expression. Assume all variables represent positive real numbers. - −2161253\sqrt [ 3 ] { - \frac { 216 } { 125 } }3−125216​​

Simplify the expression. Assume all variables represent positive real numbers. - 15⋅48\sqrt { 15 } \cdot \sqrt { 48 }15​⋅48​