Question 1

Simplify the expression.
-$$\sqrt { ( - 36 ) ^ { 2 } }$$

Accepted Answer

A)  6 
B)  $- 6$ 
C)  36 
D)  $- 36$ 
A)  6 
B)  $- 6$ 
C)  36 
D)  $- 36$

Question 2

Decide whether the expression has been simplified correctly.
-$\left( x ^ { 6 } \right) ^ { 2 } = x ^ { 8 }$

Accepted Answer

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

Question 3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 5 ) ^ { - 1 }$

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B)  5 
C)  $- \frac { 1 } { 5 }$ 
D)  $- 5$ 
A)  $\frac { 1 } { 5 }$ 
B)  5 
C)  $- \frac { 1 } { 5 }$ 
D)  $- 5$

Question 4

Solve the problem.
-$$( n + 3 ) ^ { 2 }$$

Accepted Answer

A)  $n ^ { 2 } + 9$ 
B)  $n ^ { 2 } + 6 n + 9$ 
C)  $9 n ^ { 2 } + 6 n + 9$ 
D)  $n + 9$ 
A)  $n ^ { 2 } + 9$ 
B)  $n ^ { 2 } + 6 n + 9$ 
C)  $9 n ^ { 2 } + 6 n + 9$ 
D)  $n + 9$

Question 5

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( 81 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }$$

Accepted Answer

A)  $\frac { 3 k } { m ^ { 2 } }$ 
B)  $3 \mathrm {~km} ^ { 2 }$ 
C)  $\frac { 4 k } { m ^ { 2 } }$ 
D)  $4 \mathrm {~km} ^ { 2 }$ 
A)  $\frac { 3 k } { m ^ { 2 } }$ 
B)  $3 \mathrm {~km} ^ { 2 }$ 
C)  $\frac { 4 k } { m ^ { 2 } }$ 
D)  $4 \mathrm {~km} ^ { 2 }$

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 4 ] { \frac { 625 } { 1296 } }$$

Accepted Answer

A)  $\frac { 625 } { 1296 }$ 
B)  $\frac { 125 } { 216 }$ 
C)  $\frac { 25 } { 36 }$ 
D)  $\frac { 5 } { 6 }$ 
A)  $\frac { 625 } { 1296 }$ 
B)  $\frac { 125 } { 216 }$ 
C)  $\frac { 25 } { 36 }$ 
D)  $\frac { 5 } { 6 }$

Question 7

Write the expression in lowest terms.
-$$\frac { 4 ( x - 2 ) } { ( x - 2 ) ( x - 5 ) }$$

Accepted Answer

A)  $\frac { 4 } { x - 2 }$ 
B)  $\frac { x - 2 } { x - 5 }$ 
C)  $\frac { 1 } { x - 5 }$ 
D)  $\frac { 4 } { x - 5 }$ 
A)  $\frac { 4 } { x - 2 }$ 
B)  $\frac { x - 2 } { x - 5 }$ 
C)  $\frac { 1 } { x - 5 }$ 
D)  $\frac { 4 } { x - 5 }$

Question 8

Find the product.
-$$- 2 x ^ { 5 } ( 3 x - 6 )$$

Accepted Answer

A)  $6 x ^ { 6 } - 12 x ^ { 5 }$ 
B)  $6 x ^ { 6 }$ 
C)  $- 6 x ^ { 5 } + 12$ 
D)  $- 6 x ^ { 6 } + 12 x ^ { 5 }$ 
A)  $6 x ^ { 6 } - 12 x ^ { 5 }$ 
B)  $6 x ^ { 6 }$ 
C)  $- 6 x ^ { 5 } + 12$ 
D)  $- 6 x ^ { 6 } + 12 x ^ { 5 }$

Question 9

Identify the expression as a polynomial or not a polynomial.
-$7 x - \frac { 8 } { x } + 18$

Accepted Answer

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

Question 10

Solve the equation
-$$\frac { x ^ { 2 } + 3 x - 40 } { x + 8 }$$

Accepted Answer

A)  $x ^ { 2 } + 4 x - 32$ 
B)  $x ^ { 2 } - 5$ 
C)  $x - 5$ 
D)  $x + 5$ 
A)  $x ^ { 2 } + 4 x - 32$ 
B)  $x ^ { 2 } - 5$ 
C)  $x - 5$ 
D)  $x + 5$

Question 11

Evaluate the expression.
-$\text { Let } x = 7 , y = - 7 \text {. Evaluate } 4 | x | + 5 | y | \text {. }$

Accepted Answer

A)  -63 
B)  63 
C)  -7 
D)  7 
A)  -63 
B)  63 
C)  -7 
D)  7

Question 12

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

Accepted Answer

A)  2 
B)  0 
C)  x 
D)  1 
A)  2 
B)  0 
C)  x 
D)  1

Question 13

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$x ^ { 1 / 7 } \cdot x ^ { 6 / 7 }$$

Accepted Answer

A)  $x ^ { 6 / 49 }$ 
B)  $\frac { 1 } { x }$ 
C)  $x$ 
D)  $x ^ { 6 / 7 }$ 
A)  $x ^ { 6 / 49 }$ 
B)  $\frac { 1 } { x }$ 
C)  $x$ 
D)  $x ^ { 6 / 7 }$

Question 14

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-The Blood Alcohol Concentration (BAC) of a person who has been drinking is given by the expression $$\text { number of } \mathrm { oz } \times \% \text { alcohol } \times .075 \div \text { body weight in } \mathrm { lb } \text { - hours of drinking } \times .015 \text {. }$$ Find the BAC to the nearest thousandth for a 174-lb woman, who, in 3 hours, has drunk 4 16-oz beers (64 oz), each having a 3.2% alcohol content.

Accepted Answer

A)  -0.207 
B)  0.043 
C)  -199.912 
D)  -0.023 
A)  -0.207 
B)  0.043 
C)  -199.912 
D)  -0.023

Question 15

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { y ^ { 9 / 8 } } { y ^ { 5 / 8 } }$$

Accepted Answer

A)  $y ^ { 9 / 8 }$ 
B)  $\frac { 1 } { y }$ 
C)  $\mathrm { y } ^ { 1 / 2 }$ 
D)  $\mathrm { y }$ 
A)  $y ^ { 9 / 8 }$ 
B)  $\frac { 1 } { y }$ 
C)  $\mathrm { y } ^ { 1 / 2 }$ 
D)  $\mathrm { y }$

Question 16

Solve the problem.
-$$( x + 2 y ) ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 6 x ^ { 2 } y + 12 x y ^ { 2 } + 8 y ^ { 3 }$ 
B)  $3 ( x + 2 y )$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } y + 4 x y + 4 x y ^ { 2 } + 8 y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $x ^ { 3 } + 8 y ^ { 3 }$ 
A)  $x ^ { 3 } + 6 x ^ { 2 } y + 12 x y ^ { 2 } + 8 y ^ { 3 }$ 
B)  $3 ( x + 2 y )$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } y + 4 x y + 4 x y ^ { 2 } + 8 y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $x ^ { 3 } + 8 y ^ { 3 }$

Question 17

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 8,9,10,11,12,13,14,15,16,17,18 \} , \mathrm { M } = \{ 8,10,12,14 \} , \mathrm { N } = \{ 9,11,13,15,17 \}$, $Q = \{ 8,10,12,14,16,18 \}$, and $R = \{ 8,9,10,11 \}$.

$\varnothing \cup \mathrm { N }$

Accepted Answer

A)  $\{ 8,9,10,11,12,13,14,15,16,17,18 \}$ 
B)  $\mathrm { N }$, or $\{ 9,11,13,15,17 \}$; $\mathrm { N }$ and $\varnothing$ are disjoint sets. 
C)  $\{ 10,12,14,16,18 \}$ 
D)  $\varnothing ; N$ and $\varnothing$ are disjoint sets. 
A)  $\{ 8,9,10,11,12,13,14,15,16,17,18 \}$ 
B)  $\mathrm { N }$, or $\{ 9,11,13,15,17 \}$; $\mathrm { N }$ and $\varnothing$ are disjoint sets. 
C)  $\{ 10,12,14,16,18 \}$ 
D)  $\varnothing ; N$ and $\varnothing$ are disjoint sets.

Question 18

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

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 135 } } { 3 }$ 
B)  $\frac { \sqrt [ 3 ] { 45 } } { 3 }$ 
C)  $\frac { 45 } { 3 }$ 
D)  $\frac { \sqrt [ 3 ] { 15 } } { 3 }$ 
A)  $\frac { \sqrt [ 3 ] { 135 } } { 3 }$ 
B)  $\frac { \sqrt [ 3 ] { 45 } } { 3 }$ 
C)  $\frac { 45 } { 3 }$ 
D)  $\frac { \sqrt [ 3 ] { 15 } } { 3 }$

Question 19

Solve the problem.
-$$( 7 a + 3 c ) ( 7 a - 3 c )$$

Accepted Answer

A)  $7 a ^ { 2 } - 3 c ^ { 2 }$ 
B)  $49 a ^ { 2 } - 42 a c - 9 c ^ { 2 }$ 
C)  $49 a ^ { 2 } + 42 a c - 9 c ^ { 2 }$ 
D)  $49 a ^ { 2 } - 9 c ^ { 2 }$ 
A)  $7 a ^ { 2 } - 3 c ^ { 2 }$ 
B)  $49 a ^ { 2 } - 42 a c - 9 c ^ { 2 }$ 
C)  $49 a ^ { 2 } + 42 a c - 9 c ^ { 2 }$ 
D)  $49 a ^ { 2 } - 9 c ^ { 2 }$

Question 20

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-0 {9, 10, 11, 12, 13, 14}

Accepted Answer

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

Simplify the expression. - $\sqrt { ( - 36 ) ^ { 2 } }$

Decide whether the expression has been simplified correctly. - $\left( x ^ { 6 } \right) ^ { 2 } = x ^ { 8 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 5 ) ^ { - 1 }$

Solve the problem. - $( n + 3 ) ^ { 2 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( 81 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 625 } { 1296 } }$

Write the expression in lowest terms. - $\frac { 4 ( x - 2 ) } { ( x - 2 ) ( x - 5 ) }$

Find the product. - $- 2 x ^ { 5 } ( 3 x - 6 )$

Identify the expression as a polynomial or not a polynomial. - $7 x - \frac { 8 } { x } + 18$

Solve the equation - $\frac { x ^ { 2 } + 3 x - 40 } { x + 8 }$

Evaluate the expression. - $\text { Let } x = 7 , y = - 7 \text {. Evaluate } 4 | x | + 5 | y | \text {. }$

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

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $x ^ { 1 / 7 } \cdot x ^ { 6 / 7 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { y ^ { 9 / 8 } } { y ^ { 5 / 8 } }$

Solve the problem. - $( x + 2 y ) ^ { 3 }$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 8,9,10,11,12,13,14,15,16,17,18 \} , \mathrm { M } = \{ 8,10,12,14 \} , \mathrm { N } = \{ 9,11,13,15,17 \}$ , $Q = \{ 8,10,12,14,16,18 \}$ , and $R = \{ 8,9,10,11 \}$ . $\varnothing \cup \mathrm { N }$

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

Solve the problem. - $( 7 a + 3 c ) ( 7 a - 3 c )$

Insert $\in$ or $\notin$ in the blank to make the statement is true. -0 {9, 10, 11, 12, 13, 14}

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 1: Review of Basic Concepts

Simplify the expression. - (−36)2\sqrt { ( - 36 ) ^ { 2 } }(−36)2​

Decide whether the expression has been simplified correctly. - (x6)2=x8\left( x ^ { 6 } \right) ^ { 2 } = x ^ { 8 }(x6)2=x8

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−5)−1( - 5 ) ^ { - 1 }(−5)−1

Solve the problem. - (n+3)2( n + 3 ) ^ { 2 }(n+3)2

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - (81k4 m−8)1/4\left( 81 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }(81k4 m−8)1/4

Simplify the expression. Assume all variables represent positive real numbers. - 62512964\sqrt [ 4 ] { \frac { 625 } { 1296 } }41296625​​

Write the expression in lowest terms. - 4(x−2)(x−2)(x−5)\frac { 4 ( x - 2 ) } { ( x - 2 ) ( x - 5 ) }(x−2)(x−5)4(x−2)​

Find the product. - −2x5(3x−6)- 2 x ^ { 5 } ( 3 x - 6 )−2x5(3x−6)

Identify the expression as a polynomial or not a polynomial. - 7x−8x+187 x - \frac { 8 } { x } + 187x−x8​+18

Solve the equation - x2+3x−40x+8\frac { x ^ { 2 } + 3 x - 40 } { x + 8 }x+8x2+3x−40​

Evaluate the expression. - Let x=7,y=−7. Evaluate 4∣x∣+5∣y∣. \text { Let } x = 7 , y = - 7 \text {. Evaluate } 4 | x | + 5 | y | \text {. } Let x=7,y=−7. Evaluate 4∣x∣+5∣y∣.

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 2x02 x ^ { 0 }2x0

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x1/7⋅x6/7x ^ { 1 / 7 } \cdot x ^ { 6 / 7 }x1/7⋅x6/7

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - y9/8y5/8\frac { y ^ { 9 / 8 } } { y ^ { 5 / 8 } }y5/8y9/8​

Solve the problem. - (x+2y)3( x + 2 y ) ^ { 3 }(x+2y)3

Simplify the expression. Assume all variables represent positive real numbers. - 533\sqrt [ 3 ] { \frac { 5 } { 3 } }335​​

Solve the problem. - (7a+3c)(7a−3c)( 7 a + 3 c ) ( 7 a - 3 c )(7a+3c)(7a−3c)

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. -0 {9, 10, 11, 12, 13, 14}