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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 4b
Chapter 1, Problem 4b

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. -3x-1/3
Two columns of rational exponent expressions labeled I and II with multiple-choice options matching each to equivalent radical forms.

Verified step by step guidance
1
Identify the given expression: \(-3x^{-\frac{1}{3}}\).
Recall that a rational exponent \(x^{\frac{m}{n}}\) can be rewritten as a radical: \(x^{\frac{m}{n}} = \sqrt[n]{x^m}\).
Apply this to the term \(x^{-\frac{1}{3}}\): rewrite it as \(\left(\sqrt[3]{x}\right)^{-1}\), which is the reciprocal of the cube root of \(x\).
Since the exponent is negative, rewrite \(x^{-\frac{1}{3}}\) as \(\frac{1}{x^{\frac{1}{3}}} = \frac{1}{\sqrt[3]{x}}\).
Combine the coefficient \(-3\) with the radical expression to get the equivalent radical form: \(-3 \cdot \frac{1}{\sqrt[3]{x}} = \frac{-3}{\sqrt[3]{x}}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Exponents

Rational exponents express roots and powers simultaneously, where the numerator indicates the power and the denominator indicates the root. For example, x^(m/n) means the nth root of x raised to the mth power, or (√[n]{x})^m.
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Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For instance, x^(-a) equals 1 divided by x^a, which flips the base to the denominator.
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Zero and Negative Rules

Converting Rational Exponents to Radical Expressions

To convert a rational exponent to a radical expression, rewrite x^(m/n) as the nth root of x raised to the mth power: x^(m/n) = √[n]{x^m}. This helps in matching expressions involving radicals and rational exponents.
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Rational Exponents
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