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

Key Concepts

Rational Exponents

Rational exponents are exponents that can be expressed as a fraction, where the numerator indicates the power and the denominator indicates the root. For example, an exponent of 1/3 means to take the cube root of the base. This concept is essential for converting between exponential and radical forms.

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots, and are denoted using the radical symbol (√). The expression ( -3x )^(1/3) can be rewritten as the cube root of (-3x), which is a fundamental operation in algebra. Understanding how to manipulate these expressions is crucial for solving problems involving exponents.

Properties of Exponents

The properties of exponents, such as the product of powers, power of a power, and power of a product, govern how to simplify and manipulate expressions with exponents. These rules help in transforming expressions from one form to another, such as converting rational exponents to radical forms, which is necessary for matching expressions in the given problem.