Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛2/3

Verified step by step guidance

1. Identify the expression: $\frac{\sqrt[3]{2}}{3}$.
2. Recognize that the expression is a fraction with a cube root in the numerator.
3. Understand that $\sqrt[3]{2}$ represents the cube root of 2.
4. The expression is already in its simplest form since there are no like terms to combine or further simplifications possible.
5. Conclude that the expression $\frac{\sqrt[3]{2}}{3}$ is simplified as much as possible given the conditions.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots. In this case, the expression ∛(2/3) represents the cube root of the fraction 2/3. Understanding how to manipulate and simplify radical expressions is essential for performing operations on them.

Properties of Exponents

The properties of exponents govern how to simplify expressions involving powers and roots. For instance, the cube root can be expressed as an exponent of 1/3. Familiarity with these properties allows for easier manipulation of expressions involving radicals.

Simplification of Fractions

Simplifying fractions involves reducing them to their lowest terms, which can also apply when dealing with radical expressions. In the case of ∛(2/3), recognizing that both the numerator and denominator are positive real numbers helps in understanding how to simplify or evaluate the expression effectively.