Domanda del libro di testo
In Exercises 65–92, factor completely, or state that the polynomial is prime. x3+2x2−9x−18
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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 72
Simplify by reducing the index of the radical :
Guida verificata passo dopo passo1
Recognize that the expression \( [y^3]^{1/6} \) is a radical expression written with rational exponents. The exponent \( \frac{1}{6} \) represents the sixth root.
Use the property of exponents that \( (a^m)^n = a^{m \times n} \) to combine the powers inside the expression.
Multiply the exponents: \( 3 \times \frac{1}{6} = \frac{3}{6} \). So, the expression becomes \( y^{\frac{3}{6}} \).
Simplify the fraction \( \frac{3}{6} \) to its lowest terms, which is \( \frac{1}{2} \). Now the expression is \( y^{\frac{1}{2}} \).
Recognize that \( y^{\frac{1}{2}} \) is equivalent to the square root of \( y \), or \( \sqrt{y} \). This is the simplified form with the reduced index.
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Radical and Rational Exponents
Radicals and rational exponents represent the same mathematical operation. For example, the nth root of a number can be written as that number raised to the power of 1/n. Understanding this equivalence allows simplification of expressions involving roots and fractional powers.
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04:06
Rational Exponents
Properties of Exponents
The properties of exponents, such as (a^m)^n = a^(m*n), are essential for simplifying expressions with powers raised to other powers. Applying these rules helps combine and reduce exponents efficiently, which is crucial in simplifying radical expressions.
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04:06Rational Exponents
Reducing the Index of a Radical
Reducing the index of a radical involves rewriting the expression to have a smaller root index or converting it into a simpler form using exponent rules. This process often makes the expression easier to interpret or further simplify.
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05:20Expanding Radicals
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