Here are the essential concepts you must grasp in order to answer the question correctly.
Cube Roots
The cube root of a number 'x', denoted as ∛x, is a value 'y' such that y³ = x. Understanding cube roots is essential for simplifying expressions involving them, especially when performing operations like addition or multiplication. In this question, ∛11 and its powers are used, which requires familiarity with how to manipulate these roots.
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Factoring Polynomials
Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. The expression (∛11 - 1)(∛11² + ∛11 + 1) can be recognized as a product of a difference and a sum, which can be simplified using the identity for the difference of cubes. This concept is crucial for simplifying the given expression.
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Properties of Exponents
Properties of exponents govern how to manipulate expressions involving powers. Key rules include the product of powers, power of a power, and the power of a product. In this problem, understanding how to apply these properties to cube roots and their powers is necessary for correctly performing the indicated operations and simplifying the expression.
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