Exam 6: Exponents and Polynomials

Divide the monomials. $\frac { - 9 z ^ { 9 } q ^ { 10 } } { 9 z ^ { 4 } q ^ { 7 } }$ Enter your answer as $k z ^ { a } q ^ { b }$ , where k , a , b are numbers and z , q are variables.

(Short Answer)

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Question 141

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 3 a ^ { 7 } b ^ { 4 } \right) ^ { 3 }$

(Multiple Choice)

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Question 142

Simplify the following algebraic expression and express your answer using positive exponents only. $x ^ { 6 } x ^ { - 3 }$

(Multiple Choice)

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Question 143

Evaluate the following numerical expression. $\frac { 1 } { 2 ^ { - 2 } }$

(Short Answer)

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Question 144

Special product patterns occur for problems such as $( x + y ) ^ { 2 }$ and $x ^ { 2 } + y ^ { 2 }$ .

(True/False)

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Question 145

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 $-$ 4 x )(8 $-$ 5 x )

(Multiple Choice)

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Question 146

Remove the parentheses by multiplying and then simplify by combining similar terms. $9 x \left( x ^ { 2 } - 7 x - 5 \right) + x \left( 6 x ^ { 2 } + 5 x - 5 \right)$

(Short Answer)

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Question 147

Multiply the following. (4 x )(2 x ) Enter your answer as $k x ^ { p }$ where k , p are numbers and x is a variable.

(Short Answer)

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Question 148

Write the following number in standard decimal form. $( 7.11 ) \left( 10 ^ { 4 } \right)$

(Short Answer)

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Question 149

Subtract the polynomials using a horizontal format. $10 z ^ { 5 } - 6 z + 5 \text { from } 5 z ^ { 5 } + 3 z + 8$

(Multiple Choice)

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Question 150

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }$

(Multiple Choice)

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Question 151

A negative exponent means that the power must be in the denominator.

(True/False)

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Question 152

Write the following number in scientific notation. 725

(Short Answer)

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Question 153

Perform the division and find the quotient. $\left( 3 x ^ { 2 } + 9 x - 30 \right) \div ( x + 5 )$

(Short Answer)

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Question 154

Perform the division of the polynomials by monomials. $\frac { - 30 p ^ { 9 } a - 45 p ^ { 9 } a ^ { 11 } + 10 p ^ { 9 } a ^ { 18 } } { - 5 p ^ { 9 } a }$

(Multiple Choice)

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Question 155

Perform the division. $\left( x ^ { 2 } - 6 x - 27 \right) \div ( x - 9 )$

(Short Answer)

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Question 156

Divide the polynomial by the monomial. $\frac { - 16 x ^ { 13 } + 18 x ^ { 10 } } { 2 x ^ { 2 } }$

(Short Answer)

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Question 157

Perform the division. $\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }$

(Short Answer)

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Question 158

Remove the parentheses by multiplying and then simplify by combining similar terms. $3 x \left( x ^ { 2 } - 6 x - 4 \right) + x \left( 7 x ^ { 2 } + 7 x - 4 \right)$

(Short Answer)

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Question 159

Find the indicated product by applying the distributive property and combining similar terms. (5 x $-$ 7) (5 x $-$ 8)

(Short Answer)

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Question 160

Divide the monomials. $\frac { - 9 z ^ { 9 } q ^ { 10 } } { 9 z ^ { 4 } q ^ { 7 } }$ Enter your answer as $k z ^ { a } q ^ { b }$ , where k , a , b are numbers and z , q are variables.

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 3 a ^ { 7 } b ^ { 4 } \right) ^ { 3 }$

Simplify the following algebraic expression and express your answer using positive exponents only. $x ^ { 6 } x ^ { - 3 }$

Evaluate the following numerical expression. $\frac { 1 } { 2 ^ { - 2 } }$

Special product patterns occur for problems such as $( x + y ) ^ { 2 }$ and $x ^ { 2 } + y ^ { 2 }$ .

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 $-$ 4 x )(8 $-$ 5 x )

Remove the parentheses by multiplying and then simplify by combining similar terms. $9 x \left( x ^ { 2 } - 7 x - 5 \right) + x \left( 6 x ^ { 2 } + 5 x - 5 \right)$

Multiply the following. (4 x )(2 x ) Enter your answer as $k x ^ { p }$ where k , p are numbers and x is a variable.

Write the following number in standard decimal form. $( 7.11 ) \left( 10 ^ { 4 } \right)$

Subtract the polynomials using a horizontal format. $10 z ^ { 5 } - 6 z + 5 \text { from } 5 z ^ { 5 } + 3 z + 8$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }$

A negative exponent means that the power must be in the denominator.

Write the following number in scientific notation. 725

Perform the division and find the quotient. $\left( 3 x ^ { 2 } + 9 x - 30 \right) \div ( x + 5 )$

Perform the division of the polynomials by monomials. $\frac { - 30 p ^ { 9 } a - 45 p ^ { 9 } a ^ { 11 } + 10 p ^ { 9 } a ^ { 18 } } { - 5 p ^ { 9 } a }$

Perform the division. $\left( x ^ { 2 } - 6 x - 27 \right) \div ( x - 9 )$

Divide the polynomial by the monomial. $\frac { - 16 x ^ { 13 } + 18 x ^ { 10 } } { 2 x ^ { 2 } }$

Perform the division. $\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $3 x \left( x ^ { 2 } - 6 x - 4 \right) + x \left( 7 x ^ { 2 } + 7 x - 4 \right)$

Find the indicated product by applying the distributive property and combining similar terms. (5 x $-$ 7) (5 x $-$ 8)

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

Divide the monomials. −9z9q109z4q7\frac { - 9 z ^ { 9 } q ^ { 10 } } { 9 z ^ { 4 } q ^ { 7 } }9z4q7−9z9q10​ Enter your answer as kzaqbk z ^ { a } q ^ { b }kzaqb , where k , a , b are numbers and z , q are variables.

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. (−3a7b4)3\left( - 3 a ^ { 7 } b ^ { 4 } \right) ^ { 3 }(−3a7b4)3

Simplify the following algebraic expression and express your answer using positive exponents only. x6x−3x ^ { 6 } x ^ { - 3 }x6x−3

Evaluate the following numerical expression. 12−2\frac { 1 } { 2 ^ { - 2 } }2−21​

Special product patterns occur for problems such as (x+y)2( x + y ) ^ { 2 }(x+y)2 and x2+y2x ^ { 2 } + y ^ { 2 }x2+y2 .

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 −-− 4 x )(8 −-− 5 x )

Remove the parentheses by multiplying and then simplify by combining similar terms. 9x(x2−7x−5)+x(6x2+5x−5)9 x \left( x ^ { 2 } - 7 x - 5 \right) + x \left( 6 x ^ { 2 } + 5 x - 5 \right)9x(x2−7x−5)+x(6x2+5x−5)

Multiply the following. (4 x )(2 x ) Enter your answer as kxpk x ^ { p }kxp where k , p are numbers and x is a variable.

Write the following number in standard decimal form. (7.11)(104)( 7.11 ) \left( 10 ^ { 4 } \right)(7.11)(104)

Subtract the polynomials using a horizontal format. 10z5−6z+5 from 5z5+3z+810 z ^ { 5 } - 6 z + 5 \text { from } 5 z ^ { 5 } + 3 z + 810z5−6z+5 from 5z5+3z+8

Simplify the following algebraic expression and express your answer using positive exponents only. (u−1v−2)4\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }(u−1v−2)4

A negative exponent means that the power must be in the denominator.

Write the following number in scientific notation. 725

Perform the division and find the quotient. (3x2+9x−30)÷(x+5)\left( 3 x ^ { 2 } + 9 x - 30 \right) \div ( x + 5 )(3x2+9x−30)÷(x+5)

Perform the division of the polynomials by monomials. −30p9a−45p9a11+10p9a18−5p9a\frac { - 30 p ^ { 9 } a - 45 p ^ { 9 } a ^ { 11 } + 10 p ^ { 9 } a ^ { 18 } } { - 5 p ^ { 9 } a }−5p9a−30p9a−45p9a11+10p9a18​

Perform the division. (x2−6x−27)÷(x−9)\left( x ^ { 2 } - 6 x - 27 \right) \div ( x - 9 )(x2−6x−27)÷(x−9)

Divide the polynomial by the monomial. −16x13+18x102x2\frac { - 16 x ^ { 13 } + 18 x ^ { 10 } } { 2 x ^ { 2 } }2x2−16x13+18x10​

Perform the division. 8n3−272n−3\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }2n−38n3−27​

Remove the parentheses by multiplying and then simplify by combining similar terms. 3x(x2−6x−4)+x(7x2+7x−4)3 x \left( x ^ { 2 } - 6 x - 4 \right) + x \left( 7 x ^ { 2 } + 7 x - 4 \right)3x(x2−6x−4)+x(7x2+7x−4)

Find the indicated product by applying the distributive property and combining similar terms. (5 x −-− 7) (5 x −-− 8)

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

Divide the monomials. $\frac { - 9 z ^ { 9 } q ^ { 10 } } { 9 z ^ { 4 } q ^ { 7 } }$ Enter your answer as $k z ^ { a } q ^ { b }$ , where k , a , b are numbers and z , q are variables.

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 3 a ^ { 7 } b ^ { 4 } \right) ^ { 3 }$

Simplify the following algebraic expression and express your answer using positive exponents only. $x ^ { 6 } x ^ { - 3 }$

Evaluate the following numerical expression. $\frac { 1 } { 2 ^ { - 2 } }$

Special product patterns occur for problems such as $( x + y ) ^ { 2 }$ and $x ^ { 2 } + y ^ { 2 }$ .

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 $-$ 4 x )(8 $-$ 5 x )

Remove the parentheses by multiplying and then simplify by combining similar terms. $9 x \left( x ^ { 2 } - 7 x - 5 \right) + x \left( 6 x ^ { 2 } + 5 x - 5 \right)$

Multiply the following. (4 x )(2 x ) Enter your answer as $k x ^ { p }$ where k , p are numbers and x is a variable.

Write the following number in standard decimal form. $( 7.11 ) \left( 10 ^ { 4 } \right)$

Subtract the polynomials using a horizontal format. $10 z ^ { 5 } - 6 z + 5 \text { from } 5 z ^ { 5 } + 3 z + 8$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }$

Perform the division and find the quotient. $\left( 3 x ^ { 2 } + 9 x - 30 \right) \div ( x + 5 )$

Perform the division of the polynomials by monomials. $\frac { - 30 p ^ { 9 } a - 45 p ^ { 9 } a ^ { 11 } + 10 p ^ { 9 } a ^ { 18 } } { - 5 p ^ { 9 } a }$

Perform the division. $\left( x ^ { 2 } - 6 x - 27 \right) \div ( x - 9 )$

Divide the polynomial by the monomial. $\frac { - 16 x ^ { 13 } + 18 x ^ { 10 } } { 2 x ^ { 2 } }$

Perform the division. $\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $3 x \left( x ^ { 2 } - 6 x - 4 \right) + x \left( 7 x ^ { 2 } + 7 x - 4 \right)$

Find the indicated product by applying the distributive property and combining similar terms. (5 x $-$ 7) (5 x $-$ 8)