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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 3b
Chapter 1, Problem 3b

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 matching radical expressions labeled II for a math matching exercise.

Verified step by step guidance
1
Recall that a rational exponent of the form \(a^{m/n}\) can be rewritten as a radical: \(a^{m/n} = \left( \sqrt[n]{a} \right)^m = \sqrt[n]{a^m}\).
Identify the base and the rational exponent in the expression \((-3x)^{-1/3}\). Here, the base is \(-3x\) and the exponent is \(-\frac{1}{3}\).
Rewrite the expression using the radical form: \((-3x)^{-1/3} = \frac{1}{(-3x)^{1/3}}\) because a negative exponent means the reciprocal.
Express \((-3x)^{1/3}\) as a cube root: \((-3x)^{1/3} = \sqrt[3]{-3x}\).
Combine the steps to write the original expression as \(\frac{1}{\sqrt[3]{-3x}}\), which is the equivalent radical expression.

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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, i.e., (√[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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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. Applying this helps match expressions with radicals and rational exponents.
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Related Practice
Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (d) ( 3x )-1/3

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Textbook Question

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. 3x1/3

Textbook Question

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

Textbook Question

Determine whether each statement is true or false. If false, correct the right side of the equation. (y2)(y5) = y7

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Textbook Question

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

Textbook Question

Determine whether each statement is true or false. If false, correct the right side of the equation. 5-2 = 1/52