Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 6x2−6x−12
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 74
Write each number in decimal notation without the use of exponents.
Verified step by step guidance1
Identify the given number in scientific notation: \(-3.14 \times 10^{-3}\).
Recall that \(10^{-3}\) means \(\frac{1}{10^3}\) or moving the decimal point 3 places to the left.
Start with the number 3.14 and move the decimal point 3 places to the left to convert from scientific notation to decimal notation.
Since the number is negative, keep the negative sign in front of the decimal number after moving the decimal point.
Write the final number in decimal form without exponents, ensuring the decimal point is correctly placed after moving it 3 places to the left.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Scientific Notation
Scientific notation expresses numbers as a product of a decimal number and a power of ten, making very large or small numbers easier to read and work with. For example, 3.14×10^−3 means 3.14 multiplied by 10 raised to the power of -3.
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Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive exponent. For instance, 10^−3 equals 1 divided by 10^3, or 1/1000, which helps convert numbers from scientific notation to decimal form.
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Converting Scientific Notation to Decimal Notation
To convert a number from scientific notation to decimal notation, multiply the decimal part by 10 raised to the given exponent. For negative exponents, move the decimal point to the left accordingly, turning 3.14×10^−3 into 0.00314.
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Related Practice
Textbook Question
Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.
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Textbook Question
Simplify the radical expressions in Exercises 67–74, if possible. ⁵√64x6/⁵√2x
Textbook Question
In Exercises 67–82, find each product. (9x+7y)2
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Textbook Question
In Exercises 69–82, simplify each complex rational expression. (1/x + 1/y)/(x+y)
Textbook Question
State the name of the property illustrated. 6+(−4)=(−4)+6
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