Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (k^1/3)/(k^2/3)(k^-1)

Key Concepts

Exponents and Their Properties

Understanding exponents is crucial in algebra, as they represent repeated multiplication of a base. Key properties include the product of powers (a^m * a^n = a^(m+n)), the quotient of powers (a^m / a^n = a^(m-n)), and the power of a power (a^m)^n = a^(m*n). These rules help simplify expressions involving exponents effectively.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^-n = 1/a^n. In simplification, it is essential to convert negative exponents into positive ones to express the final answer in a standard form, as specified in the question.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and applying exponent rules to reduce the expression to its simplest form. This process often includes factoring, canceling common factors, and ensuring that the final expression adheres to any given constraints, such as avoiding negative exponents in this case.