Exam 5: Exponents and Polynomials

Write the number in scientific notation. -A light-year is a measure of length defined as the distance that light travels in one year, which is about $9,500,000,000,000$ kilometers. Write this number in scientific notation.

(Multiple Choice)

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Question 141

Simplify. -If $P ( x ) = - 9 x + 7$ , find $P ( - 1 )$ .

(Multiple Choice)

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Question 142

Use synthetic division to divide. - $\left( x ^ { 2 } + 4 x - 77 \right) \div ( x - 7 )$

(Multiple Choice)

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Question 143

Use the power rule and the power of a product or quotient rule to simplify the expression. - $( - 2 a ) ^ { 6 }$

(Multiple Choice)

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Question 144

Perform the indicated operation. - $( 8 x - 6 ) + ( 10 x - 8 )$

(Multiple Choice)

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Question 145

Find the quotient using long division. - $\frac { x ^ { 2 } + 17 x + 72 } { x + 8 }$

(Multiple Choice)

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Question 146

Find the perimeter. -

(Multiple Choice)

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Question 147

Simplify. -If $P ( x ) = 9 x - 3$ , find $P ( a )$ .

(Multiple Choice)

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Question 148

Perform the indicated operation. - $\left( 6 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 12 x y + 12 y ^ { 2 } \right)$

(Multiple Choice)

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Question 149

Use the product rule to simplify the expression. Write the result using exponents. - $w ^ { 5 } \cdot w ^ { 8 } \cdot w ^ { 8 }$

(Multiple Choice)

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Question 150

Multiply. - $( b - 4 ) ( b - 8 )$

(Multiple Choice)

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Question 151

Simplify the expression. - $\left( \frac { 3 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 4 }$

(Multiple Choice)

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Question 152

Simplify the expression. Write the result using positive exponents only. - $7 ^ { - 1 } + 5 ^ { - 1 }$

(Multiple Choice)

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Question 153

Evaluate the expression. - $5 ^ { - 3 }$

(Multiple Choice)

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Question 154

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } - x + 34 ; - 3$

(Multiple Choice)

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Question 155

Multiply. - $( 3 z + 10 ) ^ { 2 }$

(Multiple Choice)

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Question 156

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $21 x y z + 25 x ^ { 2 } z - 9 y ^ { 2 } z ^ { 3 } + 5 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

(Multiple Choice)

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Question 157

Solve. -The parallelogram has base length $6 y ^ { 5 }$ meters and height $3 y ^ { 7 }$ meters. Find its area as an expression in $\mathrm { y } \cdot ( \mathrm { A } = \mathrm { b } \cdot \mathrm { h } )$ $Solve. -The parallelogram has base length 6 y ^ { 5 } meters and height 3 y ^ { 7 } meters. Find its area as an expression in \mathrm { y } \cdot ( \mathrm { A } = \mathrm { b } \cdot \mathrm { h } )$

(Multiple Choice)

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Question 158

Use the power rule to simplify the expression. - $\left( x ^ { 2 } \right) ^ { 8 }$

(Multiple Choice)

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Question 159

Perform the indicated operation. - $\left( 18 x ^ { 2 } + 11 \right) - \left( 6 x ^ { 2 } - 6 \right)$

(Multiple Choice)

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Question 160

Write the number in scientific notation. -A light-year is a measure of length defined as the distance that light travels in one year, which is about $9,500,000,000,000$ kilometers. Write this number in scientific notation.

Simplify. -If $P ( x ) = - 9 x + 7$ , find $P ( - 1 )$ .

Use synthetic division to divide. - $\left( x ^ { 2 } + 4 x - 77 \right) \div ( x - 7 )$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $( - 2 a ) ^ { 6 }$

Perform the indicated operation. - $( 8 x - 6 ) + ( 10 x - 8 )$

Find the quotient using long division. - $\frac { x ^ { 2 } + 17 x + 72 } { x + 8 }$

Find the perimeter. -

Simplify. -If $P ( x ) = 9 x - 3$ , find $P ( a )$ .

Perform the indicated operation. - $\left( 6 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 12 x y + 12 y ^ { 2 } \right)$

Use the product rule to simplify the expression. Write the result using exponents. - $w ^ { 5 } \cdot w ^ { 8 } \cdot w ^ { 8 }$

Multiply. - $( b - 4 ) ( b - 8 )$

Simplify the expression. - $\left( \frac { 3 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 4 }$

Simplify the expression. Write the result using positive exponents only. - $7 ^ { - 1 } + 5 ^ { - 1 }$

Evaluate the expression. - $5 ^ { - 3 }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } - x + 34 ; - 3$

Multiply. - $( 3 z + 10 ) ^ { 2 }$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $21 x y z + 25 x ^ { 2 } z - 9 y ^ { 2 } z ^ { 3 } + 5 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Use the power rule to simplify the expression. - $\left( x ^ { 2 } \right) ^ { 8 }$

Perform the indicated operation. - $\left( 18 x ^ { 2 } + 11 \right) - \left( 6 x ^ { 2 } - 6 \right)$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Write the number in scientific notation. -A light-year is a measure of length defined as the distance that light travels in one year, which is about 9,500,000,000,0009,500,000,000,0009,500,000,000,000 kilometers. Write this number in scientific notation.

Simplify. -If P(x)=−9x+7P ( x ) = - 9 x + 7P(x)=−9x+7 , find P(−1)P ( - 1 )P(−1) .

Use synthetic division to divide. - (x2+4x−77)÷(x−7)\left( x ^ { 2 } + 4 x - 77 \right) \div ( x - 7 )(x2+4x−77)÷(x−7)

Use the power rule and the power of a product or quotient rule to simplify the expression. - (−2a)6( - 2 a ) ^ { 6 }(−2a)6

Perform the indicated operation. - (8x−6)+(10x−8)( 8 x - 6 ) + ( 10 x - 8 )(8x−6)+(10x−8)

Find the quotient using long division. - x2+17x+72x+8\frac { x ^ { 2 } + 17 x + 72 } { x + 8 }x+8x2+17x+72​

Find the perimeter. -

Simplify. -If P(x)=9x−3P ( x ) = 9 x - 3P(x)=9x−3 , find P(a)P ( a )P(a) .

Perform the indicated operation. - (6x2−xy−y2)+(x2+12xy+12y2)\left( 6 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 12 x y + 12 y ^ { 2 } \right)(6x2−xy−y2)+(x2+12xy+12y2)

Use the product rule to simplify the expression. Write the result using exponents. - w5⋅w8⋅w8w ^ { 5 } \cdot w ^ { 8 } \cdot w ^ { 8 }w5⋅w8⋅w8

Multiply. - (b−4)(b−8)( b - 4 ) ( b - 8 )(b−4)(b−8)

Simplify the expression. - (3x3y2)4\left( \frac { 3 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 4 }(y23x3​)4

Simplify the expression. Write the result using positive exponents only. - 7−1+5−17 ^ { - 1 } + 5 ^ { - 1 }7−1+5−1

Evaluate the expression. - 5−35 ^ { - 3 }5−3

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=2x3+2x2−x+34;−3P ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } - x + 34 ; - 3P(x)=2x3+2x2−x+34;−3

Multiply. - (3z+10)2( 3 z + 10 ) ^ { 2 }(3z+10)2

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - 21xyz+25x2z−9y2z3+5xy−x2y2z221 x y z + 25 x ^ { 2 } z - 9 y ^ { 2 } z ^ { 3 } + 5 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }21xyz+25x2z−9y2z3+5xy−x2y2z2

Solve. -The parallelogram has base length 6y56 y ^ { 5 }6y5 meters and height 3y73 y ^ { 7 }3y7 meters. Find its area as an expression in y⋅(A=b⋅h)\mathrm { y } \cdot ( \mathrm { A } = \mathrm { b } \cdot \mathrm { h } )y⋅(A=b⋅h)

Use the power rule to simplify the expression. - (x2)8\left( x ^ { 2 } \right) ^ { 8 }(x2)8

Perform the indicated operation. - (18x2+11)−(6x2−6)\left( 18 x ^ { 2 } + 11 \right) - \left( 6 x ^ { 2 } - 6 \right)(18x2+11)−(6x2−6)

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Write the number in scientific notation. -A light-year is a measure of length defined as the distance that light travels in one year, which is about $9,500,000,000,000$ kilometers. Write this number in scientific notation.

Simplify. -If $P ( x ) = - 9 x + 7$ , find $P ( - 1 )$ .

Use synthetic division to divide. - $\left( x ^ { 2 } + 4 x - 77 \right) \div ( x - 7 )$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $( - 2 a ) ^ { 6 }$

Perform the indicated operation. - $( 8 x - 6 ) + ( 10 x - 8 )$

Find the quotient using long division. - $\frac { x ^ { 2 } + 17 x + 72 } { x + 8 }$

Simplify. -If $P ( x ) = 9 x - 3$ , find $P ( a )$ .

Perform the indicated operation. - $\left( 6 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 12 x y + 12 y ^ { 2 } \right)$

Use the product rule to simplify the expression. Write the result using exponents. - $w ^ { 5 } \cdot w ^ { 8 } \cdot w ^ { 8 }$

Multiply. - $( b - 4 ) ( b - 8 )$

Simplify the expression. - $\left( \frac { 3 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 4 }$

Simplify the expression. Write the result using positive exponents only. - $7 ^ { - 1 } + 5 ^ { - 1 }$

Evaluate the expression. - $5 ^ { - 3 }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } - x + 34 ; - 3$

Multiply. - $( 3 z + 10 ) ^ { 2 }$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $21 x y z + 25 x ^ { 2 } z - 9 y ^ { 2 } z ^ { 3 } + 5 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Use the power rule to simplify the expression. - $\left( x ^ { 2 } \right) ^ { 8 }$

Perform the indicated operation. - $\left( 18 x ^ { 2 } + 11 \right) - \left( 6 x ^ { 2 } - 6 \right)$