Domanda del libro di testo
Add or subtract terms whenever possible.
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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 41
Simplify each exponential expression in Exercises 23–64.
Guida verificata passo dopo passo1
Identify the expression to simplify: \(\left(\frac{-4}{x}\right)^3\).
Recall the exponent rule: \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\), which means you raise both numerator and denominator to the power of 3.
Apply the exponent to the numerator and denominator separately: \(\frac{(-4)^3}{x^3}\).
Calculate the power of the numerator: \((-4)^3 = (-4) \times (-4) \times (-4)\), which involves multiplying -4 three times.
Write the simplified expression as \(\frac{(-4)^3}{x^3}\), showing the numerator and denominator raised to the third power.
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Properties of Exponents
Understanding the properties of exponents is essential for simplifying expressions like (−4/x)^3. This includes knowing how to apply the power of a product rule, which states that (ab)^n = a^n * b^n, and the power of a quotient rule, (a/b)^n = a^n / b^n.
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04:06
Rational Exponents
Negative and Fractional Bases
When dealing with negative bases raised to powers, it is important to recognize how the exponent affects the sign. For odd exponents, the result remains negative, while for even exponents, it becomes positive. Also, understanding how to handle variables in the denominator is crucial.
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05:45Radical Expressions with Fractions
Simplifying Rational Expressions
Simplifying rational expressions involves reducing fractions and applying exponent rules to both numerator and denominator. This includes raising both parts to the given power and simplifying the resulting expression to its simplest form.
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05:07Simplifying Algebraic Expressions
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