Domanda del libro di testo
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-11, -5/6, 0, 0.75, √5, π, √64}
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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 38
Simplify each exponential expression in Exercises 23–64.
Guida verificata passo dopo passo1
Identify the given expression: \(\frac{x^{30}}{x^{-10}}\).
Recall the quotient rule for exponents: when dividing like bases, subtract the exponents, i.e., \(\frac{a^m}{a^n} = a^{m-n}\).
Apply the quotient rule to the expression: \(x^{30 - (-10)}\).
Simplify the exponent subtraction: \(30 - (-10) = 30 + 10\).
Write the simplified expression as \(x^{40}\).
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Laws of Exponents
The laws of exponents provide rules for simplifying expressions involving powers. For division, the rule states that when dividing like bases, subtract the exponents: a^m / a^n = a^(m-n). This is essential for simplifying expressions such as x^30 / x^(-10).
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04:06
Rational Exponents
Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive exponent: a^(-n) = 1 / a^n. Understanding this helps in rewriting expressions with negative exponents into more manageable forms, which is crucial when simplifying x^30 / x^(-10).
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6:37Zero and Negative Rules
Simplification of Algebraic Expressions
Simplification involves reducing expressions to their simplest form by applying algebraic rules. This includes combining like terms, applying exponent rules, and rewriting expressions for clarity. Mastery of simplification techniques ensures accurate and efficient problem solving.
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05:09Introduction to Algebraic Expressions
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