For Exercises 93-98, simplify each term of the expression....

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Key Concepts

Combining Like Terms in Radical Expressions

After simplifying radical terms, if the radicals share the same index and the same radicand, they are considered like terms. These can then be added or subtracted by combining their coefficients, much like combining like terms in algebraic expressions.

Extraction of Perfect Cube Factors

When simplifying cube roots, it's helpful to look for factors in the radicand that are perfect cubes. Once identified, the cube root of these factors can be taken out of the radical, simplifying the overall expression.

Cube Roots

Cube roots are a type of radical expression where the index is three. Simplification often involves expressing the radicand as a product of a perfect cube and another factor, which then allows the extraction of the cube root of the perfect cube.

Prime Factorization

Prime factorization is used to simplify radicals by breaking down the number inside the radical into its prime factors. This process helps in identifying perfect cubes (or other perfect powers) that can be extracted out of the radical.

Radical Expressions

Radical expressions involve roots of numbers or expressions, such as square roots, cube roots, etc. They require applying properties of radicals, such as the multiplication and division rules, to simplify or combine them into a more manageable form.

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