In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. _____ ³√(x+y)⁴

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Key Concepts

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In algebra, this often involves identifying common terms or applying special formulas, such as the difference of squares or perfect square trinomials. Understanding how to factor is essential for simplifying expressions and solving equations.

Radicals

Radicals are expressions that involve roots, such as square roots or cube roots. The notation ³√ indicates the cube root, which is the value that, when multiplied by itself three times, gives the original number. Simplifying expressions with radicals often requires knowledge of how to manipulate these roots, including rationalizing denominators and applying properties of exponents.

Exponents and Powers

Exponents represent repeated multiplication of a base number. In the expression (x+y)⁴, the exponent 4 indicates that (x+y) is multiplied by itself four times. Understanding the laws of exponents, such as the product of powers and power of a power, is crucial for simplifying expressions involving powers and radicals, as it allows for the correct manipulation of these terms.