If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. ⁵√ k²

Key Concepts

Exponential Form

Exponential form represents numbers using a base raised to a power, such as a^b, where 'a' is the base and 'b' is the exponent. This notation is useful for expressing large numbers compactly and for performing operations like multiplication and division more easily. In the context of the question, converting from radical to exponential form involves identifying the root and expressing it as a fractional exponent.

Radical Form

Radical form expresses numbers using roots, such as √a or n√a, where 'n' indicates the degree of the root. This form is particularly useful for representing non-integer solutions and simplifying expressions involving roots. In the given question, the expression ⁵√k² is in radical form, indicating the fifth root of k squared, which can be converted to exponential form.

Conversion Between Forms

The conversion between exponential and radical forms is based on the relationship between exponents and roots. Specifically, the nth root of a number can be expressed as that number raised to the power of 1/n. Understanding this relationship allows for seamless transitions between forms, enabling easier evaluation and manipulation of expressions, as required in the question.