Domanda del libro di testo
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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TOC.tableOfContents
- 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
Capitolo 1, Problema 99
In Exercises 93–102, factor and simplify each algebraic expression. (x+5)−1/2−(x+5)−3/2
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Rewrite the expression using a common base. Both terms involve the base (x + 5) raised to different exponents. Let’s rewrite the expression as: (x + 5)^(-1/2) - (x + 5)^(-3/2).
Factor out the smallest power of (x + 5) from both terms. The smallest power here is (x + 5)^(-3/2). Factoring this out gives: (x + 5)^(-3/2) * [(x + 5)^(1) - 1].
Simplify the term inside the brackets. The expression becomes: (x + 5)^(-3/2) * [(x + 5) - 1].
Combine the terms inside the brackets. Simplify (x + 5) - 1 to get x + 4. The expression now becomes: (x + 5)^(-3/2) * (x + 4).
Express the final result in simplified form. The factored and simplified expression is: (x + 4) / (x + 5)^(3/2).
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Exponents and Negative Exponents
Exponents represent repeated multiplication of a base number. A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, a^(-n) = 1/(a^n). Understanding how to manipulate negative exponents is crucial for simplifying expressions like (x+5)^(-1/2) and (x+5)^(-3/2).
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04:06
Rational Exponents
Factoring Algebraic Expressions
Factoring involves rewriting an expression as a product of its factors. This process is essential for simplifying complex algebraic expressions. In the given expression, recognizing common factors can help in reducing the terms effectively, making it easier to simplify the overall expression.
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05:09Introduction to Algebraic Expressions
Simplifying Algebraic Fractions
Simplifying algebraic fractions involves reducing the fraction to its simplest form by canceling common factors in the numerator and denominator. This process often requires factoring and understanding the properties of exponents. In the context of the given expression, simplifying will lead to a clearer and more manageable form.
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05:07Simplifying Algebraic Expressions
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