Exam 5: Exponents and Polynomials

For the given functions f(x) and g(x), perform the indicated operation. - $f ( x ) = \left( 5 x ^ { 5 } - 18 x ^ { 2 } + 2 \right) , g ( x ) = \left( 7 x ^ { 5 } + 6 x ^ { 2 } - 20 \right)$ Find $f ( x ) - g ( x )$ .

(Multiple Choice)

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Question 41

Convert the given number to scientific notation. -0.000000215019

(Multiple Choice)

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Question 42

Find the special product using the appropriate formula. - $( 2 x - 5 ) ( 2 x + 5 )$

(Multiple Choice)

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Question 43

Divide. Assume all variables are nonzero. - $- \frac { 5 x ^ { 6 } y } { 45 x ^ { 5 } y ^ { 2 } }$

(Multiple Choice)

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Question 44

Multiply. - $( x + 4 ) \left( x ^ { 2 } - x + 7 \right)$

(Multiple Choice)

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Question 45

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -A computer can do one calculation in 1.4 × 10-7 seconds. How long would it take the computer to do a million (106) calculations?

(Multiple Choice)

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Question 46

Simplify. (Assume all variables are nonzero.) - $- 5^0$

(Multiple Choice)

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Question 47

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) --5^ -2

(Multiple Choice)

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Question 48

Find the missing dividend or divisor. - $\frac { ? } { x - 11 } = 4 x - 12$

(Multiple Choice)

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Question 49

Convert the given number to scientific notation. -0.0000000381018

(Multiple Choice)

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Question 50

Simplify. - $\left( x ^ { 3 } \right) ^ { 6 } \left( x ^ { 2 } \right) ^ { 5 }$

(Multiple Choice)

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Question 51

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { a ^ { 2 } } { b ^ { - 4 } }$

(Multiple Choice)

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Question 52

Find the missing monomial, factor or term. -(?) $) ^ { 2 } = 64 x ^ { 2 } - 176 x + 121$

(Multiple Choice)

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Question 53

Find the missing factor or exponent(s). - $\left( x ^ { ? } \right) ^ { 9 } = x ^ { 90 }$

(Multiple Choice)

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Question 54

Divide. Assume all variables are nonzero. - $\frac { x ^ { 8 } y ^ { 3 } } { x ^ { 6 } y ^ { 8 } }$

(Multiple Choice)

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Question 55

Multiply. - $- 3 ( 7 x + 4 )$

(Multiple Choice)

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Question 56

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left( 3 x ^ { - 4 } y ^ { - 6 } z ^ { 5 } \right) ^ { - 5 }$

(Multiple Choice)

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Question 57

Multiply. - $- 9 x ^ { 5 } \left( - 5 x ^ { 5 } + 6 x ^ { 4 } + 2 \right)$

(Multiple Choice)

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Question 58

Find the missing factor or exponent(s). - $\left( - 3 a ^ { ? } b ^ { ? } \right) ^ { 3 } = - 27 a^{ 15} b ^ { 9 }$

(Multiple Choice)

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Question 59

Multiply. - $- 8 x y ^ { 7 } \left( 10 x y ^ { 6 } + 5 y ^ { 5 } + 5 \right)$

(Multiple Choice)

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Question 60

For the given functions f(x) and g(x), perform the indicated operation. - $f ( x ) = \left( 5 x ^ { 5 } - 18 x ^ { 2 } + 2 \right) , g ( x ) = \left( 7 x ^ { 5 } + 6 x ^ { 2 } - 20 \right)$ Find $f ( x ) - g ( x )$ .

Convert the given number to scientific notation. -0.000000215019

Find the special product using the appropriate formula. - $( 2 x - 5 ) ( 2 x + 5 )$

Divide. Assume all variables are nonzero. - $- \frac { 5 x ^ { 6 } y } { 45 x ^ { 5 } y ^ { 2 } }$

Multiply. - $( x + 4 ) \left( x ^ { 2 } - x + 7 \right)$

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -A computer can do one calculation in 1.4 × 10-7 seconds. How long would it take the computer to do a million (106) calculations?

Simplify. (Assume all variables are nonzero.) - $- 5^0$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) --5^ -2

Find the missing dividend or divisor. - $\frac { ? } { x - 11 } = 4 x - 12$

Convert the given number to scientific notation. -0.0000000381018

Simplify. - $\left( x ^ { 3 } \right) ^ { 6 } \left( x ^ { 2 } \right) ^ { 5 }$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { a ^ { 2 } } { b ^ { - 4 } }$

Find the missing monomial, factor or term. -(?) $) ^ { 2 } = 64 x ^ { 2 } - 176 x + 121$

Find the missing factor or exponent(s). - $\left( x ^ { ? } \right) ^ { 9 } = x ^ { 90 }$

Divide. Assume all variables are nonzero. - $\frac { x ^ { 8 } y ^ { 3 } } { x ^ { 6 } y ^ { 8 } }$

Multiply. - $- 3 ( 7 x + 4 )$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left( 3 x ^ { - 4 } y ^ { - 6 } z ^ { 5 } \right) ^ { - 5 }$

Multiply. - $- 9 x ^ { 5 } \left( - 5 x ^ { 5 } + 6 x ^ { 4 } + 2 \right)$

Find the missing factor or exponent(s). - $\left( - 3 a ^ { ? } b ^ { ? } \right) ^ { 3 } = - 27 a^{ 15} b ^ { 9 }$

Multiply. - $- 8 x y ^ { 7 } \left( 10 x y ^ { 6 } + 5 y ^ { 5 } + 5 \right)$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Convert the given number to scientific notation. -0.000000215019

Find the special product using the appropriate formula. - (2x−5)(2x+5)( 2 x - 5 ) ( 2 x + 5 )(2x−5)(2x+5)

Divide. Assume all variables are nonzero. - −5x6y45x5y2- \frac { 5 x ^ { 6 } y } { 45 x ^ { 5 } y ^ { 2 } }−45x5y25x6y​

Multiply. - (x+4)(x2−x+7)( x + 4 ) \left( x ^ { 2 } - x + 7 \right)(x+4)(x2−x+7)

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -A computer can do one calculation in 1.4 × 10-7 seconds. How long would it take the computer to do a million (106) calculations?

Simplify. (Assume all variables are nonzero.) - −50- 5^0−50

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) --5^ -2

Find the missing dividend or divisor. - ?x−11=4x−12\frac { ? } { x - 11 } = 4 x - 12x−11?​=4x−12

Convert the given number to scientific notation. -0.0000000381018

Simplify. - (x3)6(x2)5\left( x ^ { 3 } \right) ^ { 6 } \left( x ^ { 2 } \right) ^ { 5 }(x3)6(x2)5

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - a2b−4\frac { a ^ { 2 } } { b ^ { - 4 } }b−4a2​

Find the missing monomial, factor or term. -(?) )2=64x2−176x+121) ^ { 2 } = 64 x ^ { 2 } - 176 x + 121)2=64x2−176x+121

Find the missing factor or exponent(s). - (x?)9=x90\left( x ^ { ? } \right) ^ { 9 } = x ^ { 90 }(x?)9=x90

Divide. Assume all variables are nonzero. - x8y3x6y8\frac { x ^ { 8 } y ^ { 3 } } { x ^ { 6 } y ^ { 8 } }x6y8x8y3​

Multiply. - −3(7x+4)- 3 ( 7 x + 4 )−3(7x+4)

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (3x−4y−6z5)−5\left( 3 x ^ { - 4 } y ^ { - 6 } z ^ { 5 } \right) ^ { - 5 }(3x−4y−6z5)−5

Multiply. - −9x5(−5x5+6x4+2)- 9 x ^ { 5 } \left( - 5 x ^ { 5 } + 6 x ^ { 4 } + 2 \right)−9x5(−5x5+6x4+2)

Find the missing factor or exponent(s). - (−3a?b?)3=−27a15b9\left( - 3 a ^ { ? } b ^ { ? } \right) ^ { 3 } = - 27 a^{ 15} b ^ { 9 }(−3a?b?)3=−27a15b9

Multiply. - −8xy7(10xy6+5y5+5)- 8 x y ^ { 7 } \left( 10 x y ^ { 6 } + 5 y ^ { 5 } + 5 \right)−8xy7(10xy6+5y5+5)

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Find the special product using the appropriate formula. - $( 2 x - 5 ) ( 2 x + 5 )$

Divide. Assume all variables are nonzero. - $- \frac { 5 x ^ { 6 } y } { 45 x ^ { 5 } y ^ { 2 } }$

Multiply. - $( x + 4 ) \left( x ^ { 2 } - x + 7 \right)$

Simplify. (Assume all variables are nonzero.) - $- 5^0$

Find the missing dividend or divisor. - $\frac { ? } { x - 11 } = 4 x - 12$

Simplify. - $\left( x ^ { 3 } \right) ^ { 6 } \left( x ^ { 2 } \right) ^ { 5 }$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { a ^ { 2 } } { b ^ { - 4 } }$

Find the missing monomial, factor or term. -(?) $) ^ { 2 } = 64 x ^ { 2 } - 176 x + 121$

Find the missing factor or exponent(s). - $\left( x ^ { ? } \right) ^ { 9 } = x ^ { 90 }$

Divide. Assume all variables are nonzero. - $\frac { x ^ { 8 } y ^ { 3 } } { x ^ { 6 } y ^ { 8 } }$

Multiply. - $- 3 ( 7 x + 4 )$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left( 3 x ^ { - 4 } y ^ { - 6 } z ^ { 5 } \right) ^ { - 5 }$

Multiply. - $- 9 x ^ { 5 } \left( - 5 x ^ { 5 } + 6 x ^ { 4 } + 2 \right)$

Find the missing factor or exponent(s). - $\left( - 3 a ^ { ? } b ^ { ? } \right) ^ { 3 } = - 27 a^{ 15} b ^ { 9 }$

Multiply. - $- 8 x y ^ { 7 } \left( 10 x y ^ { 6 } + 5 y ^ { 5 } + 5 \right)$