Question 1

Simplify by writing the expression without using parentheses. $$\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$$

Accepted Answer

A)  $\frac { 1 } { a }$ 
B)  $\frac { 1 } { a ^ { 6 } }$ 
C)  $\frac { 1 } { a ^ { 6 } }$ 
D)  $\frac { 1 } { 6 a ^ { 6 } }$ 
E)  $a ^ { 6 }$ 
A)  $\frac { 1 } { a }$ 
B)  $\frac { 1 } { a ^ { 6 } }$ 
C)  $\frac { 1 } { a ^ { 6 } }$ 
D)  $\frac { 1 } { 6 a ^ { 6 } }$ 
E)  $a ^ { 6 }$

Question 2

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.00005)(1,100,000)

Accepted Answer

A) 550 
B) 55 
C) 11.5 
D) 610 
E) 61 
A) 550 
B) 55 
C) 11.5 
D) 610 
E) 61

Question 3

How many terms are contained in a monomial?

Accepted Answer

A) 4 
B) 2 
C) 5 
D) 3 
E) 1 
A) 4 
B) 2 
C) 5 
D) 3 
E) 1

Question 4

Simplify the following expression. $$\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { 8 a ^ { 18 } } { 27 }$ 
B)  $\frac { 8 a ^ { 24 } } { 27 }$ 
C)  $\frac { 2 a ^ { 11 } } { 3 a ^ { 5 } }$ 
D)  $\frac { 2 a ^ { 18 } } { 3 }$ 
E)  $\frac { 8 a ^ { 18 } } { 3 a ^ { 5 } }$ 
A)  $\frac { 8 a ^ { 18 } } { 27 }$ 
B)  $\frac { 8 a ^ { 24 } } { 27 }$ 
C)  $\frac { 2 a ^ { 11 } } { 3 a ^ { 5 } }$ 
D)  $\frac { 2 a ^ { 18 } } { 3 }$ 
E)  $\frac { 8 a ^ { 18 } } { 3 a ^ { 5 } }$

Question 5

Find the indicated product. ( a + 8 b )( x + y )

Accepted Answer

A) ax + 10 bx + ay + 9 by 
B) ax + 8 bx + ay + by 
C) ax + 8 bx + ay + 8 by 
D) ax + 9 bx + ay + 8 by 
E) ax + bx + ay + 9 by 
A) ax + 10 bx + ay + 9 by 
B) ax + 8 bx + ay + by 
C) ax + 8 bx + ay + 8 by 
D) ax + 9 bx + ay + 8 by 
E) ax + bx + ay + 9 by

Question 6

The degree of a polynomial is the same as

Accepted Answer

A) the number of terms 
B) the number of variables 
C) the sum of the degrees in all terms 
D) the degree of its term with largest degree 
E) the degree of its term with least degree 
A) the number of terms 
B) the number of variables 
C) the sum of the degrees in all terms 
D) the degree of its term with largest degree 
E) the degree of its term with least degree

Question 7

Solve the equation. $( t + 1 ) ( t + 9 ) = ( t + 4 ) ( t + 6 )$

Accepted Answer

A) 5 
B) 0 
C) 3 
D) 15 
A) 5 
B) 0 
C) 3 
D) 15

Question 8

Perform the division. $$\frac { 8 x - 2 y + 16 z } { 8 x y }$$

Accepted Answer

A)  $\frac { 3 } { 4 } + \frac { 2 z } { x y }$ 
B)  $\frac { 1 } { y } + \frac { 1 } { 4 x } + \frac { 1 } { x y }$ 
C)  $\frac { 1 } { y } - \frac { 1 } { 4 x } + \frac { 2 } { x y }$ 
D)  $\frac { 1 } { y } - \frac { 1 } { 4 x } + \frac { 2 z } { x y }$ 
E)  $\frac { 4 } { y } - \frac { 4 } { 7 x } + \frac { 2 z } { x y }$ 
A)  $\frac { 3 } { 4 } + \frac { 2 z } { x y }$ 
B)  $\frac { 1 } { y } + \frac { 1 } { 4 x } + \frac { 1 } { x y }$ 
C)  $\frac { 1 } { y } - \frac { 1 } { 4 x } + \frac { 2 } { x y }$ 
D)  $\frac { 1 } { y } - \frac { 1 } { 4 x } + \frac { 2 z } { x y }$ 
E)  $\frac { 4 } { y } - \frac { 4 } { 7 x } + \frac { 2 z } { x y }$

Question 9

Simplify the expression. $$6 \left( x ^ { 2 } - 9 x - 8 \right) - 5 \left( x ^ { 2 } - 9 x - 8 \right) + 8 \left( x ^ { 2 } - 9 x - 8 \right)$$

Accepted Answer

A)  $9 x ^ { 2 } - 171 x - 152$ 
B)  $9 x ^ { 2 } - 171 x - 72$ 
C)  $9 x ^ { 2 } - 81 x - 72$ 
D)  $9 x ^ { 2 } - 81 x - 152$ 
E) none of these 
A)  $9 x ^ { 2 } - 171 x - 152$ 
B)  $9 x ^ { 2 } - 171 x - 72$ 
C)  $9 x ^ { 2 } - 81 x - 72$ 
D)  $9 x ^ { 2 } - 81 x - 152$ 
E) none of these

Question 10

Perform the division. If there is a remainder, leave the answer in $\text { quotient } + \frac { \text { remainder } } { \text { divisor } }$ form. $\frac { 8 x ^ { 3 } + 23 x ^ { 2 } + 6 x + 2 } { 8 x + 7 }$

Accepted Answer

A)  $x ^ { 2 } + 5 x - 1 + \frac { 9 } { 8 x + 7 }$ 
B)  $x ^ { 2 } + 2 x - 7 + \frac { 9 } { 8 x + 7 }$ 
C)  $x ^ { 2 } + 1 x - \frac { 3 } { 4 } + \frac { 8 } { 8 x + 7 }$ 
D)  $x ^ { 2 } + 2 x - 1$ 
E)  $x ^ { 2 } + 2 x - 1 + \frac { 9 } { 8 x + 7 }$ 
A)  $x ^ { 2 } + 5 x - 1 + \frac { 9 } { 8 x + 7 }$ 
B)  $x ^ { 2 } + 2 x - 7 + \frac { 9 } { 8 x + 7 }$ 
C)  $x ^ { 2 } + 1 x - \frac { 3 } { 4 } + \frac { 8 } { 8 x + 7 }$ 
D)  $x ^ { 2 } + 2 x - 1$ 
E)  $x ^ { 2 } + 2 x - 1 + \frac { 9 } { 8 x + 7 }$

Question 11

Write the following expression as an expression involving only one base and one exponent. $$\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$$

Accepted Answer

A)  $16 s ^ { 10 }$ 
B)  $16 s ^ { 8 }$ 
C)  $4 s ^ { 20 }$ 
D)  $16 s ^ { 12 }$ 
E)  $16 s ^ { 20 }$ 
A)  $16 s ^ { 10 }$ 
B)  $16 s ^ { 8 }$ 
C)  $4 s ^ { 20 }$ 
D)  $16 s ^ { 12 }$ 
E)  $16 s ^ { 20 }$

Question 12

Evaluate the algebraic expression for the given values of the variables. $2 x y - x ^ { 2 } y ^ { 2 } + 6 y ^ { 2 } , x = 2 \text { and } y = - 2$

Accepted Answer

The answer of Evaluate the algebraic expression for the given...

Question 13

Divide. $\frac { y ^ { 3 } - 8 } { y - 2 }$

Accepted Answer

A)  $y ^ { 2 } - 2 y + 4$ 
B)  $y ^ { 2 } + 4 y + 4$ 
C)  $y ^ { 2 } + 2 y + 4$ 
D)  $y ^ { 2 } - 4 y + 4$ 
E) none of these 
A)  $y ^ { 2 } - 2 y + 4$ 
B)  $y ^ { 2 } + 4 y + 4$ 
C)  $y ^ { 2 } + 2 y + 4$ 
D)  $y ^ { 2 } - 4 y + 4$ 
E) none of these

Question 14

Simplify the following expression. $$\frac { 2 ^ { - 3 } } { 3 ^ { - 1 } }$$

Accepted Answer

A) 1 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 8 } { 3 }$ 
E)  $- \frac { 3 } { 8 }$ 
A) 1 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 8 } { 3 }$ 
E)  $- \frac { 3 } { 8 }$

Question 15

Simplify the following expression. $$\left( \frac { - 2 m ^ { 3 } m ^ { - 6 } } { m ^ { - 3 } m ^ { 6 } } \right) ^ { 2 }$$

Accepted Answer

A)  $4 m ^ { 12 }$ 
B)  $\frac { 1 } { 4 m ^ { 12 } }$ 
C)  $- \frac { 4 } { m ^ { 12 } }$ 
D)  $\frac { - 4 } { m ^ { 12 } }$ 
E)  $\frac { 4 } { m ^ { 12 } }$ 
A)  $4 m ^ { 12 }$ 
B)  $\frac { 1 } { 4 m ^ { 12 } }$ 
C)  $- \frac { 4 } { m ^ { 12 } }$ 
D)  $\frac { - 4 } { m ^ { 12 } }$ 
E)  $\frac { 4 } { m ^ { 12 } }$

Question 16

Find the quotient. $\frac { - 16 a b c ^ { 5 } } { 16 b c }$

Accepted Answer

A)  $- a c ^ { 5 }$ 
B)  $- a b c ^ { 6 }$ 
C)  $- a c ^ { 4 }$ 
D)  $- a c ^ { 6 }$ 
E)  $- a b c ^ { 4 }$ 
A)  $- a c ^ { 5 }$ 
B)  $- a b c ^ { 6 }$ 
C)  $- a c ^ { 4 }$ 
D)  $- a c ^ { 6 }$ 
E)  $- a b c ^ { 4 }$

Question 17

Subtract. $$\begin{array} { l } 
3 x ^ { 3 } + 4 x ^ { 2 } - 5 x + 6 \
4 x ^ { 3 } - 3 x ^ { 2 } - 8 x - 1\
\hline 
\end{array}$$

Accepted Answer

A)  $- x ^ { 3 } - x ^ { 2 } + 13 x + 7$ 
B)  $- x ^ { 3 } + 7 x ^ { 2 } + 3 x + 7$ 
C)  $x ^ { 3 } - 7 x ^ { 2 } - 13 x + 7$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } + 13 x + 7$ 
E)  $- x ^ { 3 } - x ^ { 2 } - 13 x + 7$ 
A)  $- x ^ { 3 } - x ^ { 2 } + 13 x + 7$ 
B)  $- x ^ { 3 } + 7 x ^ { 2 } + 3 x + 7$ 
C)  $x ^ { 3 } - 7 x ^ { 2 } - 13 x + 7$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } + 13 x + 7$ 
E)  $- x ^ { 3 } - x ^ { 2 } - 13 x + 7$

Question 18

Find the product. $\frac { 4 } { 3 } a ^ { 2 } b ( 6 a - 5 b )$

Accepted Answer

A)  $\frac { 8 } { 3 } a ^ { 2 } b - \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
B)  $\frac { 8 } { 3 } a ^ { 3 } b + \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
C)  $8 a ^ { 3 } b - \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
D)  $8 a ^ { 3 } b - \frac { 16 } { 3 } a b ^ { 2 }$ 
E)  $8 a ^ { 2 } b + \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
A)  $\frac { 8 } { 3 } a ^ { 2 } b - \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
B)  $\frac { 8 } { 3 } a ^ { 3 } b + \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
C)  $8 a ^ { 3 } b - \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$ 
D)  $8 a ^ { 3 } b - \frac { 16 } { 3 } a b ^ { 2 }$ 
E)  $8 a ^ { 2 } b + \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$

Question 19

In the expression $- 5 ^ { 3 }$ , what is the exponent?

Accepted Answer

The answer of In the expression \(- 5 ^ {...

Question 20

Add the monomials. 8 b + 5 b + 2 b

Accepted Answer

The answer of Add the monomials. 8 b + 5...

Simplify by writing the expression without using parentheses. $\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.00005)(1,100,000)

How many terms are contained in a monomial?

Simplify the following expression. $\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$

Find the indicated product. ( a + 8 b )( x + y )

The degree of a polynomial is the same as

Solve the equation. $( t + 1 ) ( t + 9 ) = ( t + 4 ) ( t + 6 )$

Perform the division. $\frac { 8 x - 2 y + 16 z } { 8 x y }$

Simplify the expression. $6 \left( x ^ { 2 } - 9 x - 8 \right) - 5 \left( x ^ { 2 } - 9 x - 8 \right) + 8 \left( x ^ { 2 } - 9 x - 8 \right)$

Perform the division. If there is a remainder, leave the answer in $\text { quotient } + \frac { \text { remainder } } { \text { divisor } }$ form. $\frac { 8 x ^ { 3 } + 23 x ^ { 2 } + 6 x + 2 } { 8 x + 7 }$

Write the following expression as an expression involving only one base and one exponent. $\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$

Evaluate the algebraic expression for the given values of the variables. $2 x y - x ^ { 2 } y ^ { 2 } + 6 y ^ { 2 } , x = 2 \text { and } y = - 2$

Divide. $\frac { y ^ { 3 } - 8 } { y - 2 }$

Simplify the following expression. $\frac { 2 ^ { - 3 } } { 3 ^ { - 1 } }$

Simplify the following expression. $\left( \frac { - 2 m ^ { 3 } m ^ { - 6 } } { m ^ { - 3 } m ^ { 6 } } \right) ^ { 2 }$

Find the quotient. $\frac { - 16 a b c ^ { 5 } } { 16 b c }$

Subtract. 3+4-5x+6 4-3-8x-1

Find the product. $\frac { 4 } { 3 } a ^ { 2 } b ( 6 a - 5 b )$

In the expression $- 5 ^ { 3 }$ , what is the exponent?

Add the monomials. 8 b + 5 b + 2 b

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 5: Exponents and Polynomials

Simplify by writing the expression without using parentheses. (a3a2a6)6\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }(a6a3a2​)6

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.00005)(1,100,000)

How many terms are contained in a monomial?

Simplify the following expression. (2a2⋅a3⋅a63a3⋅a2)3\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }(3a3⋅a22a2⋅a3⋅a6​)3

Find the indicated product. ( a + 8 b )( x + y )

The degree of a polynomial is the same as

Solve the equation. (t+1)(t+9)=(t+4)(t+6)( t + 1 ) ( t + 9 ) = ( t + 4 ) ( t + 6 )(t+1)(t+9)=(t+4)(t+6)

Perform the division. 8x−2y+16z8xy\frac { 8 x - 2 y + 16 z } { 8 x y }8xy8x−2y+16z​

Simplify the expression. 6(x2−9x−8)−5(x2−9x−8)+8(x2−9x−8)6 \left( x ^ { 2 } - 9 x - 8 \right) - 5 \left( x ^ { 2 } - 9 x - 8 \right) + 8 \left( x ^ { 2 } - 9 x - 8 \right)6(x2−9x−8)−5(x2−9x−8)+8(x2−9x−8)

Write the following expression as an expression involving only one base and one exponent. (4s3s4s3)2\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }(4s3s4s3)2

Evaluate the algebraic expression for the given values of the variables. 2xy−x2y2+6y2,x=2 and y=−22 x y - x ^ { 2 } y ^ { 2 } + 6 y ^ { 2 } , x = 2 \text { and } y = - 22xy−x2y2+6y2,x=2 and y=−2

Divide. y3−8y−2\frac { y ^ { 3 } - 8 } { y - 2 }y−2y3−8​

Simplify the following expression. 2−33−1\frac { 2 ^ { - 3 } } { 3 ^ { - 1 } }3−12−3​

Simplify the following expression. (−2m3m−6m−3m6)2\left( \frac { - 2 m ^ { 3 } m ^ { - 6 } } { m ^ { - 3 } m ^ { 6 } } \right) ^ { 2 }(m−3m6−2m3m−6​)2

Find the quotient. −16abc516bc\frac { - 16 a b c ^ { 5 } } { 16 b c }16bc−16abc5​

Subtract. 3+4-5x+6 4-3-8x-1

Find the product. 43a2b(6a−5b)\frac { 4 } { 3 } a ^ { 2 } b ( 6 a - 5 b )34​a2b(6a−5b)

In the expression −53- 5 ^ { 3 }−53 , what is the exponent?

Add the monomials. 8 b + 5 b + 2 b

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Simplify by writing the expression without using parentheses. $\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$

Simplify the following expression. $\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$

Solve the equation. $( t + 1 ) ( t + 9 ) = ( t + 4 ) ( t + 6 )$

Perform the division. $\frac { 8 x - 2 y + 16 z } { 8 x y }$

Simplify the expression. $6 \left( x ^ { 2 } - 9 x - 8 \right) - 5 \left( x ^ { 2 } - 9 x - 8 \right) + 8 \left( x ^ { 2 } - 9 x - 8 \right)$

Write the following expression as an expression involving only one base and one exponent. $\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$

Evaluate the algebraic expression for the given values of the variables. $2 x y - x ^ { 2 } y ^ { 2 } + 6 y ^ { 2 } , x = 2 \text { and } y = - 2$

Divide. $\frac { y ^ { 3 } - 8 } { y - 2 }$

Simplify the following expression. $\frac { 2 ^ { - 3 } } { 3 ^ { - 1 } }$

Simplify the following expression. $\left( \frac { - 2 m ^ { 3 } m ^ { - 6 } } { m ^ { - 3 } m ^ { 6 } } \right) ^ { 2 }$

Find the quotient. $\frac { - 16 a b c ^ { 5 } } { 16 b c }$

Find the product. $\frac { 4 } { 3 } a ^ { 2 } b ( 6 a - 5 b )$

In the expression $- 5 ^ { 3 }$ , what is the exponent?