Question #6450494Fill in the Blank
Algebra-2
Question
Simplify the expression , where . __________.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to simplify fourth roots by factoring the radicand into a product of a perfect fourth power and another factor.
This problem assesses the ability to simplify fourth roots by factoring the radicand into a product of a perfect fourth power and another factor.
Key Concept Explanation
The goal is to express the radical in its simplest form, where the radicand has no factors that are perfect fourth powers, and no radicals in the denominator.
The goal is to express the radical in its simplest form, where the radicand has no factors that are perfect fourth powers, and no radicals in the denominator.
Step-by-step Solution
1. Factor the radicand into a product of a perfect fourth power and another factor: , where .
2. Recognize that can be written as and is a perfect fourth power: .
3. Rewrite as where
1. Factor the radicand into a product of a perfect fourth power and another factor: , where .
2. Recognize that can be written as and is a perfect fourth power: .
3. Rewrite as where
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