Question 1

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 5 ) ^ { - 2 }$

Accepted Answer

A)  $- \frac { 1 } { 25 }$ 
B)  $- 25$ 
C)  $\frac { 1 } { 25 }$ 
D)  25 
A)  $- \frac { 1 } { 25 }$ 
B)  $- 25$ 
C)  $\frac { 1 } { 25 }$ 
D)  25

Question 2

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$9 z ^ { 4 } + 2 z ^ { 3 } - 7 z ^ { 2 } + 9$

Accepted Answer

A)  Binomial 
B)  None of these 
C)  Monomial 
D)  Trinomial 
A)  Binomial 
B)  None of these 
C)  Monomial 
D)  Trinomial

Question 3

Find the domain of the expression.
-$$\frac { 2 y } { y - x }$$

Accepted Answer

A)  $\{ y \mid y \neq 1$ and $x \mid x \neq 1 \}$ 
B)  $\{ y \mid y \neq x \}$ 
C)  $\{ y \mid y \neq 0$ and $x \mid x \neq 0 \}$ 
D)  $\{ y \mid y \neq - x \}$ 
A)  $\{ y \mid y \neq 1$ and $x \mid x \neq 1 \}$ 
B)  $\{ y \mid y \neq x \}$ 
C)  $\{ y \mid y \neq 0$ and $x \mid x \neq 0 \}$ 
D)  $\{ y \mid y \neq - x \}$

Question 4

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-

Accepted Answer

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

Question 5

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { 5 ^ { 8 } } { 5 ^ { 2 } }$$

Accepted Answer

A)  6 
B)  $\frac { 1 } { 5 ^ { 6 } }$ 
C)  $5^6$ 
D)  $25^6$ 
A)  6 
B)  $\frac { 1 } { 5 ^ { 6 } }$ 
C)  $5^6$ 
D)  $25^6$

Question 6

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

Accepted Answer

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

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { 14 m ^ { 5 } } \cdot \sqrt { 7 m ^ { 17 } }$$

Accepted Answer

A)  $7 m ^ { 12 }$ 
B)  $14 m ^ { 8 } \sqrt { 7 }$ 
C)  $7 m ^ { 11 } \sqrt { 2 }$ 
D)  $7 \mathrm {~m} ^ { 10 } \sqrt { 2 }$ 
A)  $7 m ^ { 12 }$ 
B)  $14 m ^ { 8 } \sqrt { 7 }$ 
C)  $7 m ^ { 11 } \sqrt { 2 }$ 
D)  $7 \mathrm {~m} ^ { 10 } \sqrt { 2 }$

Question 8

Identify the set as finite or infinite.
-$$\{ \mathrm { x } \mid \mathrm { x } \text { is a plant alive now } \}$$

Accepted Answer

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

Question 9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( 3 x ) ^ { - 2 }$

Accepted Answer

A)  $- 9 x ^ { 2 }$ 
B)  $\frac { 1 } { 9 x ^ { 2 } }$ 
C)  $- \frac { 1 } { 6 x }$ 
D)  $- 6 x$ 
A)  $- 9 x ^ { 2 }$ 
B)  $\frac { 1 } { 9 x ^ { 2 } }$ 
C)  $- \frac { 1 } { 6 x }$ 
D)  $- 6 x$

Question 10

Write in radical form. Assume all variables represent positive real numbers.
-$$\left( 2 m ^ { 4 } + 6 k ^ { 2 } \right) ^ { 3 / 5 }$$

Accepted Answer

A)  $\frac { 1 } { \left( \sqrt [ 3 ] { 2 m ^ { 4 } + 6 \mathrm { k } ^ { 2 } } \right) ^ { 5 } }$ 
B)  $\frac { 1 } { \left( \sqrt [ 5 ] { 2 m ^ { 4 } + 6 k ^ { 2 } } \right) ^ { 3 } }$ 
C)  $\left( \sqrt [ 5 ] { 2 m ^ { 4 } + 6 k ^ { 2 } } \right) ^ { 3 }$ 
D)  $\left( \sqrt [ 3 ] { 2 m ^ { 4 } + 6 \mathrm { k } ^ { 2 } } \right) ^ { 5 }$ 
A)  $\frac { 1 } { \left( \sqrt [ 3 ] { 2 m ^ { 4 } + 6 \mathrm { k } ^ { 2 } } \right) ^ { 5 } }$ 
B)  $\frac { 1 } { \left( \sqrt [ 5 ] { 2 m ^ { 4 } + 6 k ^ { 2 } } \right) ^ { 3 } }$ 
C)  $\left( \sqrt [ 5 ] { 2 m ^ { 4 } + 6 k ^ { 2 } } \right) ^ { 3 }$ 
D)  $\left( \sqrt [ 3 ] { 2 m ^ { 4 } + 6 \mathrm { k } ^ { 2 } } \right) ^ { 5 }$

Question 11

Factor out the greatest common factor. Simplify the factors, if possible.
-$4 x ( 5 x + 3 ) - 5 ( 5 x + 3 )$

Accepted Answer

A)  $( 4 x - 5 ) ( 5 x + 3 )$ 
B)  $( 20 x + 5 ) ( x - 3 )$ 
C)  $( 4 x + 5 ) ( 5 x - 3 )$ 
D)  $( 20 x - 5 ) ( x + 3 )$ 
A)  $( 4 x - 5 ) ( 5 x + 3 )$ 
B)  $( 20 x + 5 ) ( x - 3 )$ 
C)  $( 4 x + 5 ) ( 5 x - 3 )$ 
D)  $( 20 x - 5 ) ( x + 3 )$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { \frac { y ^ { 8 } } { 27 } }$$

Accepted Answer

A)  $3 y ^ { 2 } \sqrt [ 3 ] { y ^ { 2 } }$ 
B)  $y ^ { 2 } - 3 \sqrt [ 3 ] { y ^ { 2 } }$ 
C)  $\frac { y ^ { 2 } \sqrt [ 3 ] { y ^ { 2 } } } { 3 }$ 
D)  $\frac { y ^ { 2 } + \sqrt [ 3 ] { y ^ { 2 } } } { 3 }$ 
A)  $3 y ^ { 2 } \sqrt [ 3 ] { y ^ { 2 } }$ 
B)  $y ^ { 2 } - 3 \sqrt [ 3 ] { y ^ { 2 } }$ 
C)  $\frac { y ^ { 2 } \sqrt [ 3 ] { y ^ { 2 } } } { 3 }$ 
D)  $\frac { y ^ { 2 } + \sqrt [ 3 ] { y ^ { 2 } } } { 3 }$

Question 13

Factor by any method.
-$$y ^ { 2 } - \frac { 100 } { 121 }$$

Accepted Answer

A)  $\left\{ y + \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
B)  $\left\{ y - \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
C)  $\left\{ y + \frac { 100 } { 11 } \left( y - \frac { 100 } { 11 } \right) \right.$ 
D)  $\left\{ \mathrm { y } ^ { 2 } + \frac { 10 } { 11 } \right) \left( \mathrm { y } ^ { 2 } - \frac { 10 } { 11 } \right)$ 
A)  $\left\{ y + \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
B)  $\left\{ y - \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
C)  $\left\{ y + \frac { 100 } { 11 } \left( y - \frac { 100 } { 11 } \right) \right.$ 
D)  $\left\{ \mathrm { y } ^ { 2 } + \frac { 10 } { 11 } \right) \left( \mathrm { y } ^ { 2 } - \frac { 10 } { 11 } \right)$

Question 14

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt { \frac { 98 x ^ { 3 } } { y 5 } }$$

Accepted Answer

A)  $- \frac { x \sqrt { 98 x y } } { y ^ { 3 } }$ 
B)  $- \frac { 7 x ^ { 3 } \sqrt { 2 } } { y ^ { 5 } }$ 
C)  $- \frac { 7 x \sqrt { 2 x y } } { y ^ { 3 } }$ 
D)  $- \frac { 7 x } { y ^ { 2 } } \sqrt { \frac { 2 x } { y } }$ 
A)  $- \frac { x \sqrt { 98 x y } } { y ^ { 3 } }$ 
B)  $- \frac { 7 x ^ { 3 } \sqrt { 2 } } { y ^ { 5 } }$ 
C)  $- \frac { 7 x \sqrt { 2 x y } } { y ^ { 3 } }$ 
D)  $- \frac { 7 x } { y ^ { 2 } } \sqrt { \frac { 2 x } { y } }$

Question 15

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

Accepted Answer

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

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$$4 \sqrt [ 5 ] { m ^ { 11 } p ^ { 7 } } - 2 m ^ { 2 } p \sqrt [ 5 ] { m ^ { 2 } }$$

Accepted Answer

A)  cannot be simplified 
B)  $2 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
C)  $6 m p ^ { 2 } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$ 
D)  2 
A)  cannot be simplified 
B)  $2 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
C)  $6 m p ^ { 2 } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$ 
D)  2

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt [ 4 ] { 1296 }$$

Accepted Answer

A)  $- 6$ 
B)  $- 36$ 
C)  not a real number 
D)  $- 5$ 
A)  $- 6$ 
B)  $- 36$ 
C)  not a real number 
D)  $- 5$

Question 18

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 5 } { p ^ { 2 } - 36 } + p } { \frac { 1 } { p + 6 } }$$

Accepted Answer

A)  $\frac { 5 + p ^ { 3 } - 36 p } { p - 6 }$ 
B)  $\frac { 5 + p ^ { 2 } - 36 p } { p + 36 }$ 
C)  $\frac { 1 } { p ^ { 2 } + 6 }$ 
D)  $\frac { 5 + p ^ { 3 } + 36 p } { p }$ 
A)  $\frac { 5 + p ^ { 3 } - 36 p } { p - 6 }$ 
B)  $\frac { 5 + p ^ { 2 } - 36 p } { p + 36 }$ 
C)  $\frac { 1 } { p ^ { 2 } + 6 }$ 
D)  $\frac { 5 + p ^ { 3 } + 36 p } { p }$

Question 19

Solve the problem.
-$( a - 9 ) ( a + 9 )$

Accepted Answer

A)  $a ^ { 2 } - 18 a - 81$ 
B)  $a ^ { 2 } - 18$ 
C)  $a ^ { 2 } - 81$ 
D)  $a ^ { 2 } + 18 a - 81$ 
A)  $a ^ { 2 } - 18 a - 81$ 
B)  $a ^ { 2 } - 18$ 
C)  $a ^ { 2 } - 81$ 
D)  $a ^ { 2 } + 18 a - 81$

Question 20

Factor the trinomial, if possible.
-$$( x + 6 y ) ^ { 2 } + 10 ( x + 6 y ) + 25$$

Accepted Answer

A)  $( x - 6 y + 5 ) ^ { 2 }$ 
B)  $( x + 6 y - 5 ) ( x - 6 y + 5 )$ 
C)  $( x + 6 y + 5 ) ^ { 2 }$ 
D)  $( x + 6 y - 5 ) ^ { 2 }$ 
A)  $( x - 6 y + 5 ) ^ { 2 }$ 
B)  $( x + 6 y - 5 ) ( x - 6 y + 5 )$ 
C)  $( x + 6 y + 5 ) ^ { 2 }$ 
D)  $( x + 6 y - 5 ) ^ { 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 5 ) ^ { - 2 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $9 z ^ { 4 } + 2 z ^ { 3 } - 7 z ^ { 2 } + 9$

Find the domain of the expression. - $\frac { 2 y } { y - x }$

Insert $\in$ or $\notin$ in the blank to make the statement is true. - $Insert \in or \notin in the blank to make the statement is true. -$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 5 ^ { 8 } } { 5 ^ { 2 } }$

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

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 14 m ^ { 5 } } \cdot \sqrt { 7 m ^ { 17 } }$

Identify the set as finite or infinite. - $\{ \mathrm { x } \mid \mathrm { x } \text { is a plant alive now } \}$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 3 x ) ^ { - 2 }$

Write in radical form. Assume all variables represent positive real numbers. - $\left( 2 m ^ { 4 } + 6 k ^ { 2 } \right) ^ { 3 / 5 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $4 x ( 5 x + 3 ) - 5 ( 5 x + 3 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { y ^ { 8 } } { 27 } }$

Factor by any method. - $y ^ { 2 } - \frac { 100 } { 121 }$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { \frac { 98 x ^ { 3 } } { y 5 } }$

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

Simplify the expression. Assume all variables represent positive real numbers. - $4 \sqrt [ 5 ] { m ^ { 11 } p ^ { 7 } } - 2 m ^ { 2 } p \sqrt [ 5 ] { m ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 4 ] { 1296 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 5 } { p ^ { 2 } - 36 } + p } { \frac { 1 } { p + 6 } }$

Solve the problem. - $( a - 9 ) ( a + 9 )$

Factor the trinomial, if possible. - $( x + 6 y ) ^ { 2 } + 10 ( x + 6 y ) + 25$

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Exam 1: Review of Basic Concepts

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−5)−2( - 5 ) ^ { - 2 }(−5)−2

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 9z4+2z3−7z2+99 z ^ { 4 } + 2 z ^ { 3 } - 7 z ^ { 2 } + 99z4+2z3−7z2+9

Find the domain of the expression. - 2yy−x\frac { 2 y } { y - x }y−x2y​

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. -

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 5852\frac { 5 ^ { 8 } } { 5 ^ { 2 } }5258​

Decide whether the expression has been simplified correctly. - 40x=4x4 ^ { 0 } x = 4 x40x=4x

Simplify the expression. Assume all variables represent positive real numbers. - 14m5⋅7m17\sqrt { 14 m ^ { 5 } } \cdot \sqrt { 7 m ^ { 17 } }14m5​⋅7m17​

Identify the set as finite or infinite. - {x∣x is a plant alive now }\{ \mathrm { x } \mid \mathrm { x } \text { is a plant alive now } \}{x∣x is a plant alive now }

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (3x)−2( 3 x ) ^ { - 2 }(3x)−2

Write in radical form. Assume all variables represent positive real numbers. - (2m4+6k2)3/5\left( 2 m ^ { 4 } + 6 k ^ { 2 } \right) ^ { 3 / 5 }(2m4+6k2)3/5

Factor out the greatest common factor. Simplify the factors, if possible. - 4x(5x+3)−5(5x+3)4 x ( 5 x + 3 ) - 5 ( 5 x + 3 )4x(5x+3)−5(5x+3)

Simplify the expression. Assume all variables represent positive real numbers. - y8273\sqrt [ 3 ] { \frac { y ^ { 8 } } { 27 } }327y8​​

Factor by any method. - y2−100121y ^ { 2 } - \frac { 100 } { 121 }y2−121100​

Simplify the expression. Assume all variables represent positive real numbers. - −98x3y5- \sqrt { \frac { 98 x ^ { 3 } } { y 5 } }−y598x3​​

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

Simplify the expression. Assume all variables represent positive real numbers. - 4m11p75−2m2pm254 \sqrt [ 5 ] { m ^ { 11 } p ^ { 7 } } - 2 m ^ { 2 } p \sqrt [ 5 ] { m ^ { 2 } }45m11p7​−2m2p5m2​

Simplify the expression. Assume all variables represent positive real numbers. - −12964- \sqrt [ 4 ] { 1296 }−41296​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 5p2−36+p1p+6\frac { \frac { 5 } { p ^ { 2 } - 36 } + p } { \frac { 1 } { p + 6 } }p+61​p2−365​+p​

Solve the problem. - (a−9)(a+9)( a - 9 ) ( a + 9 )(a−9)(a+9)

Factor the trinomial, if possible. - (x+6y)2+10(x+6y)+25( x + 6 y ) ^ { 2 } + 10 ( x + 6 y ) + 25(x+6y)2+10(x+6y)+25