Domanda del libro di testo
Simplify by reducing the index of the radical :
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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 73
Simplify the radical expressions in Exercises 67–74, if possible. ⁵√64x6/⁵√2x
Guida verificata passo dopo passo1
Rewrite the given expression as a single radical: \( \frac{\sqrt[5]{64x^6}}{\sqrt[5]{2x}} = \sqrt[5]{\frac{64x^6}{2x}} \).
Simplify the fraction inside the radical: \( \frac{64x^6}{2x} = 32x^5 \).
Substitute the simplified fraction back into the radical: \( \sqrt[5]{32x^5} \).
Break the radical into two parts: \( \sqrt[5]{32} \cdot \sqrt[5]{x^5} \).
Simplify each part: \( \sqrt[5]{32} = 2 \) (since \( 2^5 = 32 \)) and \( \sqrt[5]{x^5} = x \). Combine the results to get \( 2x \).
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Radical Expressions
Radical expressions involve roots, such as square roots or cube roots, represented by the radical symbol (√). In this context, we are dealing with fifth roots, denoted as ⁵√. Understanding how to manipulate these expressions, including simplifying them and applying properties of exponents, is crucial for solving problems involving radicals.
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Radical Expressions with Fractions
Properties of Exponents
The properties of exponents are rules that govern how to handle expressions involving powers. Key properties include the product of powers (a^m * a^n = a^(m+n)) and the quotient of powers (a^m / a^n = a^(m-n)). These rules are essential for simplifying expressions with radicals, as they allow us to combine and reduce terms effectively.
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04:06Rational Exponents
Simplifying Radicals
Simplifying radicals involves reducing a radical expression to its simplest form. This often includes factoring out perfect powers from under the radical and applying the properties of exponents. For example, when simplifying ⁵√(64x^6), recognizing that 64 is a perfect fifth power (2^6) and x^6 can be expressed as (x^5)(x) helps in reducing the expression.
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5:48Adding & Subtracting Unlike Radicals by Simplifying
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