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 expressions that represent roots and powers simultaneously. An exponent in the form of a fraction, such as 1/3, indicates both a root and a power; specifically, the numerator represents the power and the denominator represents the root. For example, x^(1/3) means the cube root of x, which can also be expressed as ∛x.

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. The radical symbol (√) is used to denote these roots, and the expression can be rewritten using rational exponents. For instance, the cube root of x can be written as ∛x or x^(1/3), illustrating the relationship between radical and exponent notation.

Properties of Exponents

The properties of exponents are rules that govern how to manipulate expressions involving exponents. Key properties include the product of powers, quotient of powers, and power of a power. Understanding these properties is essential for simplifying expressions and solving equations that involve rational exponents and their corresponding radical forms.