Question 1

Find $( 3 x - 7 ) ^ { 3 }$ . Don t forget that $( 3 x - 7 ) ^ { 3 }$ means (3 x $-$ 7)(3 x $-$ 7)(3 x $-$ 7).

Accepted Answer

A)  $27 x ^ { 3 } - 189 x ^ { 2 } + 147 x - 343$ 
B)  $27 x ^ { 3 } - 189 x ^ { 2 } + 441 x - 343$ 
C)  $27 x ^ { 3 } - 63 x ^ { 2 } + 441 x - 343$ 
D)  $27 x ^ { 3 } - 63 x ^ { 2 } + 441 x + 343$ 
E)  none of these 
A)  $27 x ^ { 3 } - 189 x ^ { 2 } + 147 x - 343$ 
B)  $27 x ^ { 3 } - 189 x ^ { 2 } + 441 x - 343$ 
C)  $27 x ^ { 3 } - 63 x ^ { 2 } + 441 x - 343$ 
D)  $27 x ^ { 3 } - 63 x ^ { 2 } + 441 x + 343$ 
E)  none of these

Question 2

Perform the indicated operations. $8 p - \{ 7 p - [ 2 p - ( 9 p - 16 ) ] \}$

Accepted Answer

A)  $6 p + 16$ 
B)  $- 6 p - 16$ 
C)  $- 6 p + 1$ 
D)  $6 p - 16$ 
E)  $- 6 p + 16$ 
A)  $6 p + 16$ 
B)  $- 6 p - 16$ 
C)  $- 6 p + 1$ 
D)  $6 p - 16$ 
E)  $- 6 p + 16$

Question 3

Perform the division and find the remainder. $\frac { 1 + 2 y ^ { 2 } - 5 y } { y + 2 }$

Accepted Answer

A)  $19$ 
B)  $- 19$ 
C)  $17$ 
D)  $- 17$ 
E)  $18$ 
A)  $19$ 
B)  $- 19$ 
C)  $17$ 
D)  $- 17$ 
E)  $18$

Question 4

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 3 a ^ { 6 } b ^ { 8 } \right) ^ { 3 }$

Accepted Answer

A)  $- 27 a ^ { 9 } b ^ { 11 }$ 
B)  $- 27 a ^ { 18 } b ^ { 8 }$ 
C)  $- 27 a ^ { 18 } b ^ { 24 }$ 
D)  $- 27 a ^ { 6 } b ^ { 24 }$ 
A)  $- 27 a ^ { 9 } b ^ { 11 }$ 
B)  $- 27 a ^ { 18 } b ^ { 8 }$ 
C)  $- 27 a ^ { 18 } b ^ { 24 }$ 
D)  $- 27 a ^ { 6 } b ^ { 24 }$

Question 5

Divide the polynomial by the monomial. $\frac { 4 z c - 28 z ^ { 13 } c ^ { 15 } + 12 z ^ { 20 } c ^ { 19 } } { - 4 z c }$

Accepted Answer

A)  $- z c + 7 z ^ { 12 } c ^ { 14 } - 3 z ^ { 19 } c ^ { 18 }$ 
B)  $z c + 7 z ^ { 12 } c ^ { 14 } - 3 z ^ { 19 } c ^ { 18 }$ 
C)  $- 1 + 7 z ^ { 12 } c ^ { 15 } - 3 z ^ { 20 } c ^ { 18 }$ 
D)  $- 1 + 7 z ^ { 13 } c ^ { 16 } - 3 z ^ { 19 } c ^ { 20 }$ 
E)  $- 1 + 7 z ^ { 12 } c ^ { 14 } - 3 z ^ { 19 } c ^ { 18 }$ 
A)  $- z c + 7 z ^ { 12 } c ^ { 14 } - 3 z ^ { 19 } c ^ { 18 }$ 
B)  $z c + 7 z ^ { 12 } c ^ { 14 } - 3 z ^ { 19 } c ^ { 18 }$ 
C)  $- 1 + 7 z ^ { 12 } c ^ { 15 } - 3 z ^ { 20 } c ^ { 18 }$ 
D)  $- 1 + 7 z ^ { 13 } c ^ { 16 } - 3 z ^ { 19 } c ^ { 20 }$ 
E)  $- 1 + 7 z ^ { 12 } c ^ { 14 } - 3 z ^ { 19 } c ^ { 18 }$

Question 6

Perform the division of the polynomials by monomials. $\frac { 55 x ^ { 3 } c ^ { 11 } - 50 x ^ { 14 } c ^ { 14 } + 15 x ^ { 17 } c ^ { 20 } } { - 5 x c ^ { 2 } }$

Accepted Answer

A)  $- 21 x ^ { 2 } c ^ { 9 } + 10 x ^ { 13 } c ^ { 12 } + 3 x ^ { 16 } c ^ { 18 }$ 
B)  $11 x ^ { 2 } c ^ { 9 } - 10 x ^ { 13 } c ^ { 12 } + 3 x ^ { 16 } c ^ { 18 }$ 
C)  $- 11 x ^ { 2 } c ^ { 9 } + 10 x ^ { 13 } c ^ { 14 } - 3 x ^ { 29 } c ^ { 34 }$ 
D)  $- 11 x ^ { 2 } c ^ { 9 } + 10 x ^ { 13 } c ^ { 12 } - 3 x ^ { 16 } c ^ { 18 }$ 
A)  $- 21 x ^ { 2 } c ^ { 9 } + 10 x ^ { 13 } c ^ { 12 } + 3 x ^ { 16 } c ^ { 18 }$ 
B)  $11 x ^ { 2 } c ^ { 9 } - 10 x ^ { 13 } c ^ { 12 } + 3 x ^ { 16 } c ^ { 18 }$ 
C)  $- 11 x ^ { 2 } c ^ { 9 } + 10 x ^ { 13 } c ^ { 14 } - 3 x ^ { 29 } c ^ { 34 }$ 
D)  $- 11 x ^ { 2 } c ^ { 9 } + 10 x ^ { 13 } c ^ { 12 } - 3 x ^ { 16 } c ^ { 18 }$

Question 7

Multiply by using the distributive property. $2 x ( 5 x + 9 )$

Accepted Answer

The answer of Multiply by using the distributive property. \(2...

Question 8

Multiply by using the distributive property. $- 6 x \left( 6 x ^ { 2 } - 4 x - 8 \right)$

Accepted Answer

The answer of Multiply by using the distributive property. \(-...

Question 9

Multiply the following. $\left( 4 y ^ { 5 } \right) ( 6 y ) \left( 9 y ^ { 3 } \right)$ Enter your answer as $k y^{b}$ where k and b are numbers and y is a variable.

Accepted Answer

The answer of Multiply the following. \(\left( 4 y ^...

Question 10

Perform the indicated operations. $5 z - [ 2 z - ( 8 z - 9 ) ]$

Accepted Answer

The answer of Perform the indicated operations. \(5 z -...

Question 11

Evaluate the numerical expression. $3 ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { 81 }$ 
B)  81 
C)  $\frac { 1 } { 27 }$ 
A)  $\frac { 1 } { 81 }$ 
B)  81 
C)  $\frac { 1 } { 27 }$

Question 12

Remove the parentheses by multiplying and then simplify by combining similar terms. $- 4 ( 3 x + 6 ) - 6 [ 3 x - ( 8 x + 6 ) ]$

Accepted Answer

A)  18 x + 12 
B)  23 x + 12 
C)  23 x + 60 
D)  23 x - 60 
E)  18 x - 60 
A)  18 x + 12 
B)  23 x + 12 
C)  23 x + 60 
D)  23 x - 60 
E)  18 x - 60

Question 13

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 5 a ^ { 2 } b ^ { 5 } \right) ^ { - 1 }$

Accepted Answer

A)  $\frac { 5 } { a ^ { 3 } b ^ { 6 } }$ 
B)  $\frac { 6 } { a ^ { 2 } b ^ { 6 } }$ 
C)  $\frac { 1 } { 5 a ^ { 3 } b ^ { 5 } }$ 
D)  $\frac { 1 } { 5 a ^ { 2 } b ^ { 5 } }$ 
A)  $\frac { 5 } { a ^ { 3 } b ^ { 6 } }$ 
B)  $\frac { 6 } { a ^ { 2 } b ^ { 6 } }$ 
C)  $\frac { 1 } { 5 a ^ { 3 } b ^ { 5 } }$ 
D)  $\frac { 1 } { 5 a ^ { 2 } b ^ { 5 } }$

Question 14

Add the polynomials. $6 z ^ { 4 } + 9 z + 10 \text { and } - 6 z ^ { 4 } - 7 z + 10$

Accepted Answer

A)  $2 z - 20$ 
B)  $2 z + 20$ 
C)  $12 z ^ { 4 } + 2 z + 20$ 
A)  $2 z - 20$ 
B)  $2 z + 20$ 
C)  $12 z ^ { 4 } + 2 z + 20$

Question 15

Perform the indicated operations. $\left( x ^ { 2 } - 4 x - 8 \right) + \left( 8 x ^ { 2 } - 7 x - 6 \right) - \left( 5 x ^ { 2 } - 4 x - 6 \right)$

Accepted Answer

A)  $- 4 x ^ { 2 } - 7 x + 8$ 
B)  $4 x ^ { 2 } + 7 x - 8$ 
C)  $4 x ^ { 2 } - 7 x + 8$ 
D)  $4 x ^ { 2 } - 7 x - 8$ 
A)  $- 4 x ^ { 2 } - 7 x + 8$ 
B)  $4 x ^ { 2 } + 7 x - 8$ 
C)  $4 x ^ { 2 } - 7 x + 8$ 
D)  $4 x ^ { 2 } - 7 x - 8$

Question 16

Perform the indicated operations. $( 2 p + 5 ) - ( 3 p - 10 ) + ( 8 p + 4 )$

Accepted Answer

The answer of Perform the indicated operations. \(( 2 p...

Question 17

Simplify the following algebraic expression and express your answer using positive exponents only. $\frac { y ^ { - 5 } } { y ^ { 7 } }$

Accepted Answer

A)  $y ^ { 2 }$ 
B)  $\frac { 1 } { y ^ { 12 } }$ 
C)  $\frac { 1 } { y ^ { 2 } }$ 
D)  $y ^ { 12 }$ 
A)  $y ^ { 2 }$ 
B)  $\frac { 1 } { y ^ { 12 } }$ 
C)  $\frac { 1 } { y ^ { 2 } }$ 
D)  $y ^ { 12 }$

Question 18

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 4 x ^ { - 3 } \right) \left( 9 x ^ { 8 } \right)$

Accepted Answer

The answer of Simplify the following algebraic expression and express...

Question 19

Represent the area of the shaded region in the following figure, where a = 6, b = 7, c = 2 and d = 3.

Accepted Answer

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

Question 20

Determine the degree of the polynomial. $3 y ^ { 5 } + 8 y ^ { 3 } + 11 y$

Accepted Answer

A)  9 
B)  3 
C)  5 
D)  15 
A)  9 
B)  3 
C)  5 
D)  15

Find $( 3 x - 7 ) ^ { 3 }$ . Don t forget that $( 3 x - 7 ) ^ { 3 }$ means (3 x $-$ 7)(3 x $-$ 7)(3 x $-$ 7).

Perform the indicated operations. $8 p - \{ 7 p - [ 2 p - ( 9 p - 16 ) ] \}$

Perform the division and find the remainder. $\frac { 1 + 2 y ^ { 2 } - 5 y } { y + 2 }$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 3 a ^ { 6 } b ^ { 8 } \right) ^ { 3 }$

Divide the polynomial by the monomial. $\frac { 4 z c - 28 z ^ { 13 } c ^ { 15 } + 12 z ^ { 20 } c ^ { 19 } } { - 4 z c }$

Perform the division of the polynomials by monomials. $\frac { 55 x ^ { 3 } c ^ { 11 } - 50 x ^ { 14 } c ^ { 14 } + 15 x ^ { 17 } c ^ { 20 } } { - 5 x c ^ { 2 } }$

Multiply by using the distributive property. $2 x ( 5 x + 9 )$

Multiply by using the distributive property. $- 6 x \left( 6 x ^ { 2 } - 4 x - 8 \right)$

Multiply the following. $\left( 4 y ^ { 5 } \right) ( 6 y ) \left( 9 y ^ { 3 } \right)$ Enter your answer as $k y^{b}$ where k and b are numbers and y is a variable.

Perform the indicated operations. $5 z - [ 2 z - ( 8 z - 9 ) ]$

Evaluate the numerical expression. $3 ^ { - 4 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $- 4 ( 3 x + 6 ) - 6 [ 3 x - ( 8 x + 6 ) ]$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 5 a ^ { 2 } b ^ { 5 } \right) ^ { - 1 }$

Add the polynomials. $6 z ^ { 4 } + 9 z + 10 \text { and } - 6 z ^ { 4 } - 7 z + 10$

Perform the indicated operations. $\left( x ^ { 2 } - 4 x - 8 \right) + \left( 8 x ^ { 2 } - 7 x - 6 \right) - \left( 5 x ^ { 2 } - 4 x - 6 \right)$

Perform the indicated operations. $( 2 p + 5 ) - ( 3 p - 10 ) + ( 8 p + 4 )$

Simplify the following algebraic expression and express your answer using positive exponents only. $\frac { y ^ { - 5 } } { y ^ { 7 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 4 x ^ { - 3 } \right) \left( 9 x ^ { 8 } \right)$

Represent the area of the shaded region in the following figure, where a = 6, b = 7, c = 2 and d = 3.

Determine the degree of the polynomial. $3 y ^ { 5 } + 8 y ^ { 3 } + 11 y$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 6: Exponents and Polynomials

Find (3x−7)3( 3 x - 7 ) ^ { 3 }(3x−7)3 . Don t forget that (3x−7)3( 3 x - 7 ) ^ { 3 }(3x−7)3 means (3 x −-− 7)(3 x −-− 7)(3 x −-− 7).

Perform the indicated operations. 8p−{7p−[2p−(9p−16)]}8 p - \{ 7 p - [ 2 p - ( 9 p - 16 ) ] \}8p−{7p−[2p−(9p−16)]}

Perform the division and find the remainder. 1+2y2−5yy+2\frac { 1 + 2 y ^ { 2 } - 5 y } { y + 2 }y+21+2y2−5y​

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. (−3a6b8)3\left( - 3 a ^ { 6 } b ^ { 8 } \right) ^ { 3 }(−3a6b8)3

Divide the polynomial by the monomial. 4zc−28z13c15+12z20c19−4zc\frac { 4 z c - 28 z ^ { 13 } c ^ { 15 } + 12 z ^ { 20 } c ^ { 19 } } { - 4 z c }−4zc4zc−28z13c15+12z20c19​

Perform the division of the polynomials by monomials. 55x3c11−50x14c14+15x17c20−5xc2\frac { 55 x ^ { 3 } c ^ { 11 } - 50 x ^ { 14 } c ^ { 14 } + 15 x ^ { 17 } c ^ { 20 } } { - 5 x c ^ { 2 } }−5xc255x3c11−50x14c14+15x17c20​

Multiply by using the distributive property. 2x(5x+9)2 x ( 5 x + 9 )2x(5x+9)

Multiply by using the distributive property. −6x(6x2−4x−8)- 6 x \left( 6 x ^ { 2 } - 4 x - 8 \right)−6x(6x2−4x−8)

Multiply the following. (4y5)(6y)(9y3)\left( 4 y ^ { 5 } \right) ( 6 y ) \left( 9 y ^ { 3 } \right)(4y5)(6y)(9y3) Enter your answer as kybk y^{b}kyb where k and b are numbers and y is a variable.

Perform the indicated operations. 5z−[2z−(8z−9)]5 z - [ 2 z - ( 8 z - 9 ) ]5z−[2z−(8z−9)]

Evaluate the numerical expression. 3−43 ^ { - 4 }3−4

Remove the parentheses by multiplying and then simplify by combining similar terms. −4(3x+6)−6[3x−(8x+6)]- 4 ( 3 x + 6 ) - 6 [ 3 x - ( 8 x + 6 ) ]−4(3x+6)−6[3x−(8x+6)]

Simplify the following algebraic expression and express your answer using positive exponents only. (5a2b5)−1\left( 5 a ^ { 2 } b ^ { 5 } \right) ^ { - 1 }(5a2b5)−1

Add the polynomials. 6z4+9z+10 and −6z4−7z+106 z ^ { 4 } + 9 z + 10 \text { and } - 6 z ^ { 4 } - 7 z + 106z4+9z+10 and −6z4−7z+10

Perform the indicated operations. (x2−4x−8)+(8x2−7x−6)−(5x2−4x−6)\left( x ^ { 2 } - 4 x - 8 \right) + \left( 8 x ^ { 2 } - 7 x - 6 \right) - \left( 5 x ^ { 2 } - 4 x - 6 \right)(x2−4x−8)+(8x2−7x−6)−(5x2−4x−6)

Perform the indicated operations. (2p+5)−(3p−10)+(8p+4)( 2 p + 5 ) - ( 3 p - 10 ) + ( 8 p + 4 )(2p+5)−(3p−10)+(8p+4)

Simplify the following algebraic expression and express your answer using positive exponents only. y−5y7\frac { y ^ { - 5 } } { y ^ { 7 } }y7y−5​

Simplify the following algebraic expression and express your answer using positive exponents only. (4x−3)(9x8)\left( 4 x ^ { - 3 } \right) \left( 9 x ^ { 8 } \right)(4x−3)(9x8)

Represent the area of the shaded region in the following figure, where a = 6, b = 7, c = 2 and d = 3.

Determine the degree of the polynomial. 3y5+8y3+11y3 y ^ { 5 } + 8 y ^ { 3 } + 11 y3y5+8y3+11y

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Find $( 3 x - 7 ) ^ { 3 }$ . Don t forget that $( 3 x - 7 ) ^ { 3 }$ means (3 x $-$ 7)(3 x $-$ 7)(3 x $-$ 7).

Perform the indicated operations. $8 p - \{ 7 p - [ 2 p - ( 9 p - 16 ) ] \}$

Perform the division and find the remainder. $\frac { 1 + 2 y ^ { 2 } - 5 y } { y + 2 }$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 3 a ^ { 6 } b ^ { 8 } \right) ^ { 3 }$

Divide the polynomial by the monomial. $\frac { 4 z c - 28 z ^ { 13 } c ^ { 15 } + 12 z ^ { 20 } c ^ { 19 } } { - 4 z c }$

Perform the division of the polynomials by monomials. $\frac { 55 x ^ { 3 } c ^ { 11 } - 50 x ^ { 14 } c ^ { 14 } + 15 x ^ { 17 } c ^ { 20 } } { - 5 x c ^ { 2 } }$

Multiply by using the distributive property. $2 x ( 5 x + 9 )$

Multiply by using the distributive property. $- 6 x \left( 6 x ^ { 2 } - 4 x - 8 \right)$

Multiply the following. $\left( 4 y ^ { 5 } \right) ( 6 y ) \left( 9 y ^ { 3 } \right)$ Enter your answer as $k y^{b}$ where k and b are numbers and y is a variable.

Perform the indicated operations. $5 z - [ 2 z - ( 8 z - 9 ) ]$

Evaluate the numerical expression. $3 ^ { - 4 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $- 4 ( 3 x + 6 ) - 6 [ 3 x - ( 8 x + 6 ) ]$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 5 a ^ { 2 } b ^ { 5 } \right) ^ { - 1 }$

Add the polynomials. $6 z ^ { 4 } + 9 z + 10 \text { and } - 6 z ^ { 4 } - 7 z + 10$

Perform the indicated operations. $\left( x ^ { 2 } - 4 x - 8 \right) + \left( 8 x ^ { 2 } - 7 x - 6 \right) - \left( 5 x ^ { 2 } - 4 x - 6 \right)$

Perform the indicated operations. $( 2 p + 5 ) - ( 3 p - 10 ) + ( 8 p + 4 )$

Simplify the following algebraic expression and express your answer using positive exponents only. $\frac { y ^ { - 5 } } { y ^ { 7 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 4 x ^ { - 3 } \right) \left( 9 x ^ { 8 } \right)$

Determine the degree of the polynomial. $3 y ^ { 5 } + 8 y ^ { 3 } + 11 y$