Here are the essential concepts you must grasp in order to answer the question correctly.
Cube Roots
A cube root of a number 'x' is a value 'y' such that y³ = x. This means that when 'y' is multiplied by itself three times, it equals 'x'. For example, the cube root of 8 is 2, since 2³ = 8. Understanding cube roots is essential for solving problems involving cubic equations or expressions.
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Imaginary Roots with the Square Root Property
Rational Numbers
Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In the case of 1/125, both 1 and 125 are integers, making it a rational number. Recognizing rational numbers is important when dealing with roots, as they can often simplify calculations.
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Properties of Exponents
The properties of exponents govern how to manipulate expressions involving powers. For cube roots, the property states that (a/b)^(1/3) = a^(1/3) / b^(1/3). This property allows us to separate the numerator and denominator when finding roots, making it easier to compute the cube root of fractions like 1/125.
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