Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (c) ( 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. Understanding rational exponents is crucial for converting between exponential and radical forms.

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots, and are represented using the radical symbol (√). The expression (3x)^(1/3) can be rewritten as the cube root of (3x), which is denoted as ∛(3x). Recognizing how to manipulate and interpret radical expressions is essential 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, provide rules for simplifying expressions involving exponents. For instance, (a^m)(a^n) = a^(m+n) and (ab)^n = a^n * b^n. Mastery of these properties allows for efficient simplification and transformation of expressions, including those with rational exponents.