Domanda del libro di testo
Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
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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 11
Evaluate each exponential expression in Exercises 1–22. 4−3
Guida verificata passo dopo passo1
Identify the base and the exponent in the expression \(4^{-3}\). Here, the base is 4 and the exponent is -3.
Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\), where \(a\) is a nonzero number and \(n\) is a positive integer.
Apply the negative exponent rule to rewrite \(4^{-3}\) as \(\frac{1}{4^3}\).
Calculate the positive exponent part \$4^3$ by multiplying 4 by itself three times: \(4 \times 4 \times 4\).
Express the final answer as \(\frac{1}{4^3}\), which is \(\frac{1}{64}\) after evaluating the multiplication.
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Exponents and Powers
Exponents indicate how many times a base number is multiplied by itself. For example, 4^3 means 4 × 4 × 4. Understanding this helps in evaluating expressions with positive exponents.
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04:10
Powers of i
Negative Exponents
A negative exponent means taking the reciprocal of the base raised to the corresponding positive exponent. For instance, 4^(-3) equals 1 divided by 4^3, which is 1/64.
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6:37Zero and Negative Rules
Evaluating Exponential Expressions
To evaluate an exponential expression, calculate the power indicated by the exponent, considering the sign of the exponent. This involves applying rules for both positive and negative exponents to simplify the expression.
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03:11Evaluating Algebraic Expressions
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