Textbook Question
In Exercises 91–100, simplify using properties of exponents. (3y1/4)3/y1/12
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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 101
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (2.4×10^−2)/(4.8×10^-6)
Verified step by step guidance1
Identify the given expression: \( \frac{2.4 \times 10^{-2}}{4.8 \times 10^{-6}} \).
Separate the coefficients and the powers of ten: \( \frac{2.4}{4.8} \times \frac{10^{-2}}{10^{-6}} \).
Simplify the coefficients: \( \frac{2.4}{4.8} \).
Apply the quotient rule for exponents: \( 10^{-2} \div 10^{-6} = 10^{-2 - (-6)} = 10^{4} \).
Combine the simplified coefficient with the power of ten to express the result in scientific notation.
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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 is a way of expressing numbers that are too large or too small in a compact form. It is written as a product of a number (the coefficient) between 1 and 10 and a power of ten. For example, 2.4 × 10^−2 means 2.4 divided by 100, or 0.024. This notation simplifies calculations and comparisons of very large or very small values.
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Division of Exponents
When dividing numbers in scientific notation, you divide the coefficients and subtract the exponents of the powers of ten. For instance, in the expression (2.4 × 10^−2) / (4.8 × 10^−6), you would first divide 2.4 by 4.8, and then subtract -6 from -2, resulting in a new exponent. This property of exponents is crucial for simplifying expressions in scientific notation.
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Rounding in Scientific Notation
Rounding is often necessary when working with scientific notation to ensure that the coefficient is expressed to a specific number of decimal places. In this case, the problem specifies rounding the decimal factor to two decimal places. This means that after performing the division, if the coefficient has more than two decimal places, it should be rounded accordingly to maintain precision and clarity in the final answer.
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Related Practice
Textbook Question
In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]
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Textbook Question
Factor completely, or state that the polynomial is prime. 3x^4-12x^2
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Textbook Question
In Exercises 93–102, factor and simplify each algebraic expression. (x+5)−1/2−(x+5)−3/2
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Textbook Question
Simplify by reducing the index of the radical.
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Textbook Question
Factor and simplify each algebraic expression.
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