Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜∛2

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, and higher-order roots. The notation ∜ and ∛ indicates the fourth root and cube root, respectively. Understanding how to manipulate these expressions is essential for performing operations like addition, subtraction, multiplication, and division involving radicals.

Properties of Exponents

The properties of exponents are rules that govern how to simplify expressions involving powers. For instance, the rule a^(m/n) represents the n-th root of a raised to the m-th power. This concept is crucial when dealing with radical expressions, as it allows for the conversion between radical and exponential forms, facilitating easier calculations.

Simplifying Radicals

Simplifying radicals involves reducing radical expressions to their simplest form. This includes factoring out perfect squares, cubes, or higher powers from under the radical sign. Mastery of this concept is important for accurately performing operations on radicals, ensuring that the final answer is expressed in the most concise and manageable way.