Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or fourth roots, and are represented using the radical symbol (√). In this context, ∜m² denotes the fourth root of m squared. Understanding how to manipulate these expressions is crucial for performing operations like multiplication and simplification.

Properties of Exponents

The properties of exponents govern how to handle expressions involving powers. For instance, when multiplying like bases, you add the exponents. In the case of radicals, the expression ∜m² can be rewritten using fractional exponents, specifically m^(2/4) or m^(1/2), which aids in simplifying the operation.

Multiplication of Radicals

When multiplying radical expressions, the product of the radicands (the numbers or expressions inside the radical) can be taken under a single radical. For example, ∜m² • ∜m² can be combined as ∜(m² • m²), which simplifies to ∜(m^4). This principle is essential for simplifying the expression correctly.