Question 1

Simplify the following algebraic expression and express your answer using positive exponents only. $a ^ { - 1 } a ^ { - 5 }$

Accepted Answer

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

Question 2

Find the indicated product by applying the distributive property and combining similar terms. ( x + 9)( x + 6)

Accepted Answer

The answer of Find the indicated product by applying the...

Question 3

Perform the indicated operations and simplify. $\left( - 5 x ^ { 4 } y ^ { 4 } \right) ^ { 3 } \left( - x y ^ { 3 } \right) ^ { 3 }$

Accepted Answer

A)  $125 x ^ { 15 } y ^ { 21 }$ 
B)  $- 125 x ^ { 15 } y ^ { 21 }$ 
C)  $125 x ^ { 15 } y ^ { 3 }$ 
D)  $- 125 x ^ { 10 } y ^ { 16 }$ 
E)  $125 x ^ { 10 } y ^ { 15 }$ 
A)  $125 x ^ { 15 } y ^ { 21 }$ 
B)  $- 125 x ^ { 15 } y ^ { 21 }$ 
C)  $125 x ^ { 15 } y ^ { 3 }$ 
D)  $- 125 x ^ { 10 } y ^ { 16 }$ 
E)  $125 x ^ { 10 } y ^ { 15 }$

Question 4

Scientific notation is a convenient way to represent very small and very large numbers.

Accepted Answer

A) True 
 B)False

Question 5

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ ; $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ ; $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $( 3 x - 2 ) ^ { 2 }$

Accepted Answer

A)  $9 x ^ { 2 } + 12 x + 4$ 
B)  $9 x ^ { 2 } - 12 x + 4$ 
C)  $9 x ^ { 2 } - 6 x + 4$ 
D)  $9 x ^ { 2 } - 12 x + 2$ 
E)  none of these 
A)  $9 x ^ { 2 } + 12 x + 4$ 
B)  $9 x ^ { 2 } - 12 x + 4$ 
C)  $9 x ^ { 2 } - 6 x + 4$ 
D)  $9 x ^ { 2 } - 12 x + 2$ 
E)  none of these

Question 6

Find the indicated product by applying the distributive property and combining similar terms. ( n $-$ 5) ( n $-$ 7)

Accepted Answer

A)  $13 n + 35$ 
B)  $n ^ { 2 } - 12 n - 35$ 
C)  $n ^ { 2 } - 12 n$ 
D)  $n ^ { 2 } - 12 n + 35$ 
E)  $n ^ { 2 } + 12 n + 35$ 
A)  $13 n + 35$ 
B)  $n ^ { 2 } - 12 n - 35$ 
C)  $n ^ { 2 } - 12 n$ 
D)  $n ^ { 2 } - 12 n + 35$ 
E)  $n ^ { 2 } + 12 n + 35$

Question 7

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 10 } } { b ^ { - 3 } } \right) ^ { - 1 }$

Accepted Answer

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

Question 8

Multiply the following. $\left( - 6 a b ^ { 3 } c \right) \left( 14 a ^ { 5 } c \right)$

Accepted Answer

A)  $- 84 a ^ { 5 } b ^ { 4 } c ^ { 2 }$ 
B)  $- 84 a ^ { 6 } b ^ { 3 } c$ 
C)  $- 84 a ^ { 6 } b ^ { 3 } c ^ { 2 }$ 
D)  $- 84 a ^ { 6 } b ^ { 4 } c ^ { 2 }$ 
A)  $- 84 a ^ { 5 } b ^ { 4 } c ^ { 2 }$ 
B)  $- 84 a ^ { 6 } b ^ { 3 } c$ 
C)  $- 84 a ^ { 6 } b ^ { 3 } c ^ { 2 }$ 
D)  $- 84 a ^ { 6 } b ^ { 4 } c ^ { 2 }$

Question 9

Perform the indicated operations. $( n - 5 ) - \left( 8 n ^ { 2 } - n + 1 \right) + \left( n ^ { 2 } - 9 \right)$

Accepted Answer

A)  $- 7 n ^ { 2 } + 2 n - 15$ 
B)  $- 7 n ^ { 2 } + 15$ 
C)  $- 7 n ^ { 2 } - 15$ 
D)  $- 7 n ^ { 2 } + 2 n + 15$ 
A)  $- 7 n ^ { 2 } + 2 n - 15$ 
B)  $- 7 n ^ { 2 } + 15$ 
C)  $- 7 n ^ { 2 } - 15$ 
D)  $- 7 n ^ { 2 } + 2 n + 15$

Question 10

Perform the division of the polynomials by monomials. $\frac { 14 x ^ { 9 } + 63 x ^ { 10 } } { 7 x ^ { 2 } }$

Accepted Answer

The answer of Perform the division of the polynomials by...

Question 11

The degree of a monomial is the sum of the exponents of the literal factors.

Accepted Answer

A) True 
 B)False

Question 12

Find the indicated products by using the shortcut pattern for multiplying binomials. (4 x + 9)(8 x $-$ 2)

Accepted Answer

The answer of Find the indicated products by using the...

Question 13

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ ; $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ ; $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $( 3 x - 2 ) ^ { 2 }$

Accepted Answer

The answer of Use one of the appropriate patterns \((...

Question 14

Divide the polynomial by the monomial. $\frac { 16 x ^ { 15 } + 20 x ^ { 11 } + 24 x ^ { 5 } } { 4 x ^ { 4 } }$

Accepted Answer

The answer of Divide the polynomial by the monomial. \(\frac...

Question 15

Perform the indicated operations. $\left( x ^ { 2 } - 8 x - 4 \right) + \left( 8 x ^ { 2 } - 2 x - 4 \right) - \left( 3 x ^ { 2 } - 8 x - 3 \right)$

Accepted Answer

A)  $6 x ^ { 2 } - 2 x - 11$ 
B)  $6 x ^ { 2 } + 2 x - 5$ 
C)  $6 x ^ { 2 } - 2 x - 5$ 
D)  $- 6 x ^ { 2 } - 2 x + 11$ 
E)  $6 x ^ { 2 } - 2 x + 5$ 
A)  $6 x ^ { 2 } - 2 x - 11$ 
B)  $6 x ^ { 2 } + 2 x - 5$ 
C)  $6 x ^ { 2 } - 2 x - 5$ 
D)  $- 6 x ^ { 2 } - 2 x + 11$ 
E)  $6 x ^ { 2 } - 2 x + 5$

Question 16

Determine the degree of the polynomial. $10 p ^ { 5 } + 5 p ^ { 3 } + 15 p$ degree = __________

Accepted Answer

The answer of Determine the degree of the polynomial. \(10...

Question 17

Multiply the following. $$\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 5 } x ^ { 2 } y ^ { 2 } \right)$$

Accepted Answer

A)  $\frac { 2 } { 5 } x ^ { 3 } y ^ { 2 }$ 
B)  $\frac { 2 } { 5 } x ^ { 2 } y ^ { 3 }$ 
C)  $\frac { 2 } { 5 } x ^ { 3 } y ^ { 4 }$ 
D)  $\frac { 2 } { 5 } x ^ { 2 } y ^ { 2 }$ 
E)  $\frac { 2 } { 5 } x ^ { 3 } y ^ { 3 }$ 
A)  $\frac { 2 } { 5 } x ^ { 3 } y ^ { 2 }$ 
B)  $\frac { 2 } { 5 } x ^ { 2 } y ^ { 3 }$ 
C)  $\frac { 2 } { 5 } x ^ { 3 } y ^ { 4 }$ 
D)  $\frac { 2 } { 5 } x ^ { 2 } y ^ { 2 }$ 
E)  $\frac { 2 } { 5 } x ^ { 3 } y ^ { 3 }$

Question 18

Use scientific notation and the properties of exponents to evaluate the following numerical expression. $\frac { ( 0.000038 ) ( 60 ) } { ( 0.0019 ) ( 30 ) }$ Enter your answer as a decimal.

Accepted Answer

The answer of Use scientific notation and the properties of...

Question 19

Divide the polynomial by the monomial. $\frac { 63 y ^ { 4 } a ^ { 9 } - 56 y ^ { 11 } a ^ { 14 } + 35 y ^ { 17 } a ^ { 19 } } { - 7 y a ^ { 4 } }$

Accepted Answer

A)  $- 9 y ^ { 3 } a ^ { 5 } + 8 y ^ { 10 } a ^ { 10 } - 5 y ^ { 16 } a ^ { 15 }$ 
B)  $- 9 y ^ { 4 } a ^ { 5 } + 8 y ^ { 10 } a ^ { 10 } + 5 y ^ { 16 } a ^ { 15 }$ 
C)  $9 y ^ { 3 } a ^ { 5 } - 8 y ^ { 10 } a ^ { 10 } + 5 y ^ { 16 } a ^ { 15 }$ 
D)  $- 9 y ^ { 3 } a ^ { 5 } + 8 y ^ { 10 } a ^ { 13 } - 5 y ^ { 26 } a ^ { 31 }$ 
E)  $9 y ^ { 3 } a ^ { 5 } - 8 y ^ { 10 } a ^ { 10 } + 5 y ^ { - 16 } a ^ { 15 }$ 
A)  $- 9 y ^ { 3 } a ^ { 5 } + 8 y ^ { 10 } a ^ { 10 } - 5 y ^ { 16 } a ^ { 15 }$ 
B)  $- 9 y ^ { 4 } a ^ { 5 } + 8 y ^ { 10 } a ^ { 10 } + 5 y ^ { 16 } a ^ { 15 }$ 
C)  $9 y ^ { 3 } a ^ { 5 } - 8 y ^ { 10 } a ^ { 10 } + 5 y ^ { 16 } a ^ { 15 }$ 
D)  $- 9 y ^ { 3 } a ^ { 5 } + 8 y ^ { 10 } a ^ { 13 } - 5 y ^ { 26 } a ^ { 31 }$ 
E)  $9 y ^ { 3 } a ^ { 5 } - 8 y ^ { 10 } a ^ { 10 } + 5 y ^ { - 16 } a ^ { 15 }$

Question 20

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 4 x - 9 \right)$

Accepted Answer

The answer of Find the indicated product by applying the...

Simplify the following algebraic expression and express your answer using positive exponents only. $a ^ { - 1 } a ^ { - 5 }$

Find the indicated product by applying the distributive property and combining similar terms. ( x + 9)( x + 6)

Perform the indicated operations and simplify. $\left( - 5 x ^ { 4 } y ^ { 4 } \right) ^ { 3 } \left( - x y ^ { 3 } \right) ^ { 3 }$

Scientific notation is a convenient way to represent very small and very large numbers.

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ ; $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ ; $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $( 3 x - 2 ) ^ { 2 }$

Find the indicated product by applying the distributive property and combining similar terms. ( n $-$ 5) ( n $-$ 7)

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 10 } } { b ^ { - 3 } } \right) ^ { - 1 }$

Multiply the following. $\left( - 6 a b ^ { 3 } c \right) \left( 14 a ^ { 5 } c \right)$

Perform the indicated operations. $( n - 5 ) - \left( 8 n ^ { 2 } - n + 1 \right) + \left( n ^ { 2 } - 9 \right)$

Perform the division of the polynomials by monomials. $\frac { 14 x ^ { 9 } + 63 x ^ { 10 } } { 7 x ^ { 2 } }$

The degree of a monomial is the sum of the exponents of the literal factors.

Find the indicated products by using the shortcut pattern for multiplying binomials. (4 x + 9)(8 x $-$ 2)

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ ; $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ ; $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $( 3 x - 2 ) ^ { 2 }$

Divide the polynomial by the monomial. $\frac { 16 x ^ { 15 } + 20 x ^ { 11 } + 24 x ^ { 5 } } { 4 x ^ { 4 } }$

Perform the indicated operations. $\left( x ^ { 2 } - 8 x - 4 \right) + \left( 8 x ^ { 2 } - 2 x - 4 \right) - \left( 3 x ^ { 2 } - 8 x - 3 \right)$

Determine the degree of the polynomial. $10 p ^ { 5 } + 5 p ^ { 3 } + 15 p$ degree = __________

Multiply the following. $\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 5 } x ^ { 2 } y ^ { 2 } \right)$

Use scientific notation and the properties of exponents to evaluate the following numerical expression. $\frac { ( 0.000038 ) ( 60 ) } { ( 0.0019 ) ( 30 ) }$ Enter your answer as a decimal.

Divide the polynomial by the monomial. $\frac { 63 y ^ { 4 } a ^ { 9 } - 56 y ^ { 11 } a ^ { 14 } + 35 y ^ { 17 } a ^ { 19 } } { - 7 y a ^ { 4 } }$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 4 x - 9 \right)$

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

Simplify the following algebraic expression and express your answer using positive exponents only. a−1a−5a ^ { - 1 } a ^ { - 5 }a−1a−5

Find the indicated product by applying the distributive property and combining similar terms. ( x + 9)( x + 6)

Perform the indicated operations and simplify. (−5x4y4)3(−xy3)3\left( - 5 x ^ { 4 } y ^ { 4 } \right) ^ { 3 } \left( - x y ^ { 3 } \right) ^ { 3 }(−5x4y4)3(−xy3)3

Scientific notation is a convenient way to represent very small and very large numbers.

Find the indicated product by applying the distributive property and combining similar terms. ( n −-− 5) ( n −-− 7)

Simplify the following algebraic expression and express your answer using positive exponents only. (u−10b−3)−1\left( \frac { u ^ { - 10 } } { b ^ { - 3 } } \right) ^ { - 1 }(b−3u−10​)−1

Multiply the following. (−6ab3c)(14a5c)\left( - 6 a b ^ { 3 } c \right) \left( 14 a ^ { 5 } c \right)(−6ab3c)(14a5c)

Perform the indicated operations. (n−5)−(8n2−n+1)+(n2−9)( n - 5 ) - \left( 8 n ^ { 2 } - n + 1 \right) + \left( n ^ { 2 } - 9 \right)(n−5)−(8n2−n+1)+(n2−9)

Perform the division of the polynomials by monomials. 14x9+63x107x2\frac { 14 x ^ { 9 } + 63 x ^ { 10 } } { 7 x ^ { 2 } }7x214x9+63x10​

The degree of a monomial is the sum of the exponents of the literal factors.

Find the indicated products by using the shortcut pattern for multiplying binomials. (4 x + 9)(8 x −-− 2)

Divide the polynomial by the monomial. 16x15+20x11+24x54x4\frac { 16 x ^ { 15 } + 20 x ^ { 11 } + 24 x ^ { 5 } } { 4 x ^ { 4 } }4x416x15+20x11+24x5​

Perform the indicated operations. (x2−8x−4)+(8x2−2x−4)−(3x2−8x−3)\left( x ^ { 2 } - 8 x - 4 \right) + \left( 8 x ^ { 2 } - 2 x - 4 \right) - \left( 3 x ^ { 2 } - 8 x - 3 \right)(x2−8x−4)+(8x2−2x−4)−(3x2−8x−3)

Determine the degree of the polynomial. 10p5+5p3+15p10 p ^ { 5 } + 5 p ^ { 3 } + 15 p10p5+5p3+15p degree = __________

Multiply the following. (23xy)(35x2y2)\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 5 } x ^ { 2 } y ^ { 2 } \right)(32​xy)(53​x2y2)

Use scientific notation and the properties of exponents to evaluate the following numerical expression. (0.000038)(60)(0.0019)(30)\frac { ( 0.000038 ) ( 60 ) } { ( 0.0019 ) ( 30 ) }(0.0019)(30)(0.000038)(60)​ Enter your answer as a decimal.

Divide the polynomial by the monomial. 63y4a9−56y11a14+35y17a19−7ya4\frac { 63 y ^ { 4 } a ^ { 9 } - 56 y ^ { 11 } a ^ { 14 } + 35 y ^ { 17 } a ^ { 19 } } { - 7 y a ^ { 4 } }−7ya463y4a9−56y11a14+35y17a19​

Find the indicated product by applying the distributive property and combining similar terms. (x+8)(x2−4x−9)( x + 8 ) \left( x ^ { 2 } - 4 x - 9 \right)(x+8)(x2−4x−9)

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

Simplify the following algebraic expression and express your answer using positive exponents only. $a ^ { - 1 } a ^ { - 5 }$

Perform the indicated operations and simplify. $\left( - 5 x ^ { 4 } y ^ { 4 } \right) ^ { 3 } \left( - x y ^ { 3 } \right) ^ { 3 }$

Find the indicated product by applying the distributive property and combining similar terms. ( n $-$ 5) ( n $-$ 7)

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 10 } } { b ^ { - 3 } } \right) ^ { - 1 }$

Multiply the following. $\left( - 6 a b ^ { 3 } c \right) \left( 14 a ^ { 5 } c \right)$

Perform the indicated operations. $( n - 5 ) - \left( 8 n ^ { 2 } - n + 1 \right) + \left( n ^ { 2 } - 9 \right)$

Perform the division of the polynomials by monomials. $\frac { 14 x ^ { 9 } + 63 x ^ { 10 } } { 7 x ^ { 2 } }$

Find the indicated products by using the shortcut pattern for multiplying binomials. (4 x + 9)(8 x $-$ 2)

Divide the polynomial by the monomial. $\frac { 16 x ^ { 15 } + 20 x ^ { 11 } + 24 x ^ { 5 } } { 4 x ^ { 4 } }$

Perform the indicated operations. $\left( x ^ { 2 } - 8 x - 4 \right) + \left( 8 x ^ { 2 } - 2 x - 4 \right) - \left( 3 x ^ { 2 } - 8 x - 3 \right)$

Determine the degree of the polynomial. $10 p ^ { 5 } + 5 p ^ { 3 } + 15 p$ degree = __________

Multiply the following. $\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 5 } x ^ { 2 } y ^ { 2 } \right)$

Use scientific notation and the properties of exponents to evaluate the following numerical expression. $\frac { ( 0.000038 ) ( 60 ) } { ( 0.0019 ) ( 30 ) }$ Enter your answer as a decimal.

Divide the polynomial by the monomial. $\frac { 63 y ^ { 4 } a ^ { 9 } - 56 y ^ { 11 } a ^ { 14 } + 35 y ^ { 17 } a ^ { 19 } } { - 7 y a ^ { 4 } }$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 4 x - 9 \right)$